comparison_method stringclasses 1
value | prediction_source stringclasses 1
value | output_family stringclasses 1
value | input_set stringclasses 1
value | model_family stringclasses 1
value | eval_config_base stringclasses 1
value | eval_config stringclasses 1
value | train_config stringclasses 1
value | model_name stringclasses 1
value | theory_file stringclasses 56
values | lemma_name stringlengths 18 302 | lemma_command stringlengths 26 3.61k | lemma_object stringlengths 19 2.29k | template stringlengths 10 1.16k | symbols listlengths 0 22 | types listlengths 0 22 | defs listlengths 0 19 | template_predictions_greedy listlengths 1 1 | template_levenshtein_scores_greedy int64 1 1.16k | template_success_greedy bool 1
class | isabelle_template_matches_greedy listlengths 1 1 | isabelle_template_match_count_greedy int64 0 0 | isabelle_template_success_greedy bool 1
class | isabelle_template_full_success_greedy bool 1
class | isabelle_template_success_count int64 0 0 | isabelle_template_any_success bool 1
class | isabelle_template_full_success_count int64 0 0 | isabelle_template_full_any_success bool 1
class |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.MCSs_are_possibilities | lemma (in classical_logic) MCSs_are_possibilities:
assumes "MCS s"
shows "possibility (\<lambda> x. x \<in> s)" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.maximally_consistent_set deduction implication falsum s\<rbrakk> \<Longrightarrow> classical_logic.possibility deduction implication falsum (\<lambda>x. x \<in> s) | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4\<rbrakk> \<Longrightarrow> H3 x_1 x_2 x_3 (\<lambda>y_0. y_0 \<in> x_4) | [
"Arbitrage_Probability_Correspondence.classical_logic.possibility",
"Classical_Logic.classical_logic.maximally_consistent_set",
"Classical_Logic.class.classical_logic"
] | [
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> bool)\n \\<Rightarrow> bool",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarro... | [
"class classical_logic = implication_logic +\n fixes falsum :: \"'a\" (\\<open>\\<bottom>\\<close>)\n assumes double_negation: \"\\<turnstile> (((\\<phi> \\<rightarrow> \\<bottom>) \\<rightarrow> \\<bottom>) \\<rightarrow> \\<phi>)\""
] | [
"\\<lbrakk> ?H1 ?H2 x_1 x_2; ?H1 ?H3 x_1 x_2\\<rbrakk> \\<Longrightarrow> ?H2 x_2 \\<and> ?H3 x_2 \\<and> (\\<forall>y_0. ?H1 ?H2 x_1 y_0 \\<longrightarrow> ?H1 ?H3 x_1 y_0) \\<and> (\\<forall>y_1. ?H1 ?H2 x_1 y_1 \\<longrightarrow> ?H1 ?H3 x_1 y_1) \\<and> (\\<forall>y_2. ?H1 ?H2 x_1 y_2 \\<longrightarrow> ?H1 ?H3... | 242 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.ask_revenue_equivalence | lemma (in classical_logic) ask_revenue_equivalence:
assumes "possibility p"
shows " \<pi> p \<lparr> asks = asks', bids = bids' \<rparr>
= - settle p (bids'\<^sup>\<sim> @ asks')
+ total_price asks'
+ length bids'
- total_price bids'" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.possibility deduction implication falsum p\<rbrakk> \<Longrightarrow> \<pi> p \<lparr>asks = asks', bids = bids'\<rparr> = - settle p (classical_logic.negate_bets implication falsum bids' @ asks') + total_price asks' + real (length bids') - to... | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4\<rbrakk> \<Longrightarrow> H3 x_4 (H4 x_5 x_6 H5) = H6 (H7 (H7 (H8 (H9 x_4 (H10 (H11 x_2 x_3 x_6) x_5))) (H12 x_5)) (H13 (H14 x_6))) (H12 x_6) | [
"List.length",
"Real.real",
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.classical_logic.negate_bets",
"List.append",
"Arbitrage_Probability_Correspondence.settle",
"Groups.uminus_class.uminus",
"Groups.plus_class.plus",
"Groups.minus_class.minus",
"Pro... | [
"'a list \\<Rightarrow> nat",
"nat \\<Rightarrow> real",
"'a bet_offer list \\<Rightarrow> real",
"('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n\\<Rightarrow> 'a \\<Rightarrow> ('a, 'b) bet_offer_scheme list\n \\<Rightarrow> ('a, 'b) bet_offer_scheme list",
"'a list \\<Rightarrow>... | [
"abbreviation length :: \"'a list \\<Rightarrow> nat\" where\n\"length \\<equiv> size\"",
"abbreviation real :: \"nat \\<Rightarrow> real\"\n where \"real \\<equiv> of_nat\"",
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> ... | [
"\\<lbrakk> ?H1 x_1 x_2 x_3; ?H2 x_1 x_2 x_3 x_4; ?H3 x_4 (?H4 ?H5 ?H5 x_3) = ?H6 (?H7 (?H8 (?H9 x_4 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_3 (?H10 (?H11 x_2 x_"
] | 151 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.bid_revenue_equivalence | lemma (in classical_logic) bid_revenue_equivalence:
assumes "possibility p"
shows " \<pi> p \<lparr> asks = asks', bids = bids' \<rparr>
= settle p (asks'\<^sup>\<sim> @ bids')
+ total_price asks'
- total_price bids'
- length asks'" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.possibility deduction implication falsum p\<rbrakk> \<Longrightarrow> \<pi> p \<lparr>asks = asks', bids = bids'\<rparr> = settle p (classical_logic.negate_bets implication falsum asks' @ bids') + total_price asks' - total_price bids' - real (... | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4\<rbrakk> \<Longrightarrow> H3 x_4 (H4 x_5 x_6 H5) = H6 (H6 (H7 (H8 x_4 (H9 (H10 x_2 x_3 x_5) x_6)) (H11 x_5)) (H11 x_6)) (H12 (H13 x_5)) | [
"List.length",
"Real.real",
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.classical_logic.negate_bets",
"List.append",
"Arbitrage_Probability_Correspondence.settle",
"Groups.plus_class.plus",
"Groups.minus_class.minus",
"Product_Type.Unity",
"Arbitrage_P... | [
"'a list \\<Rightarrow> nat",
"nat \\<Rightarrow> real",
"'a bet_offer list \\<Rightarrow> real",
"('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n\\<Rightarrow> 'a \\<Rightarrow> ('a, 'b) bet_offer_scheme list\n \\<Rightarrow> ('a, 'b) bet_offer_scheme list",
"'a list \\<Rightarrow>... | [
"abbreviation length :: \"'a list \\<Rightarrow> nat\" where\n\"length \\<equiv> size\"",
"abbreviation real :: \"nat \\<Rightarrow> real\"\n where \"real \\<equiv> of_nat\"",
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> ... | [
"\\<lbrakk> ?H1 x_1 x_2 x_3; ?H2 x_1 x_2 x_3 x_4; ?H3 x_4 (?H4 ?H5 ?H5 x_3) \\<le> ?H6 (?H7 (?H8 x_4 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 (?H10 x_2 x_3 (?H9 x_5))))"
] | 155 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.possibilities_are_MCS | lemma (in classical_logic) possibilities_are_MCS:
assumes "possibility p"
shows "MCS {x. p x}" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.possibility deduction implication falsum p\<rbrakk> \<Longrightarrow> classical_logic.maximally_consistent_set deduction implication falsum {x. p x} | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4\<rbrakk> \<Longrightarrow> H3 x_1 x_2 x_3 (H4 x_4) | [
"Set.Collect",
"Classical_Logic.classical_logic.maximally_consistent_set",
"Arbitrage_Probability_Correspondence.classical_logic.possibility",
"Classical_Logic.class.classical_logic"
] | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarrow> 'a set \\<Rightarrow> bool",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<R... | [
"class classical_logic = implication_logic +\n fixes falsum :: \"'a\" (\\<open>\\<bottom>\\<close>)\n assumes double_negation: \"\\<turnstile> (((\\<phi> \\<rightarrow> \\<bottom>) \\<rightarrow> \\<bottom>) \\<rightarrow> \\<phi>)\""
] | [
"\\<lbrakk> ?H1 x_1 x_2 x_3; ?H2 x_1 x_2 x_3; x_1 x_4\\<rbrakk> \\<Longrightarrow> ?H3 x_1 x_2 x_3 (?H4 (\\<lambda>y_0. y_0 \\<in> ?H4 x_1 \\<and> x_1 y_0)) \\<and> ?H3 x_1 x_2 x_3 (?H4 (\\<lambda>y_1. y_1 \\<in> ?H4 x_1 \\<and> x_1 y_1 \\<and> x_1 (x_2 y_1 x_4))) \\<and> ?H3 x_1 x_2 x_3 (?H4 (\\<lambda>y_2. y_2 \\... | 207 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.possibilities_logical_closure | lemma (in classical_logic) possibilities_logical_closure:
assumes "possibility p"
and "{x. p x} \<tturnstile> \<phi>"
shows "p \<phi>" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.possibility deduction implication falsum p; implication_logic.set_deduction deduction implication {x. p x} \<phi>\<rbrakk> \<Longrightarrow> p \<phi> | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4; H3 x_1 x_2 (H4 x_4) x_5\<rbrakk> \<Longrightarrow> x_4 x_5 | [
"Set.Collect",
"Implication_Logic.implication_logic.set_deduction",
"Arbitrage_Probability_Correspondence.classical_logic.possibility",
"Classical_Logic.class.classical_logic"
] | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a set \\<Rightarrow> 'a \\<Rightarrow> bool",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<R... | [
"class implication_logic =\n fixes deduction :: \"'a \\<Rightarrow> bool\" (\\<open>\\<turnstile> _\\<close> [60] 55)\n fixes implication :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixr \\<open>\\<rightarrow>\\<close> 70)\n assumes axiom_k: \"\\<turnstile> \\<phi> \\<rightarrow> \\<psi> \\<rightarrow> \\<p... | [
"?H1 x_1 x_2 x_3 \\<Longrightarrow> ?H2 x_1 x_2 x_3 (?H3 x_1 x_2) = ?H2 x_1 x_2 x_3 (?H3 x_1 x_2) \\<and> ?H4 x_1 x_2 (?H5 x_1) x_3 = ?H4 x_1 x_2 (?H5 x_1) x_3"
] | 96 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.classical_logic.possibility_negation | lemma (in classical_logic) possibility_negation:
assumes "possibility p"
shows "p (\<phi> \<rightarrow> \<bottom>) = (\<not> p \<phi>)" | \<lbrakk>class.classical_logic deduction implication falsum; classical_logic.possibility deduction implication falsum p\<rbrakk> \<Longrightarrow> p (implication \<phi> falsum) = (\<not> p \<phi>) | \<lbrakk>H1 x_1 x_2 x_3; H2 x_1 x_2 x_3 x_4\<rbrakk> \<Longrightarrow> x_4 (x_2 x_5 x_3) = (\<not> x_4 x_5) | [
"Arbitrage_Probability_Correspondence.classical_logic.possibility",
"Classical_Logic.class.classical_logic"
] | [
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> bool)\n \\<Rightarrow> bool",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarro... | [] | [
"?H1 x_1 x_2 x_3 \\<Longrightarrow> ?H2 x_1 x_2 x_3 x_4 = x_1 x_3"
] | 57 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.arbitrageur_correspondence | theorem (in consistent_classical_logic) arbitrageur_correspondence:
" (0 < \<pi>\<^sub>m\<^sub>i\<^sub>n \<lparr> asks = asks', bids = bids' \<rparr>)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>asks'. \<P> (bet b)) + total_price bids'
< (\<Sum>s\<leftarrow>bids'. \<P> (bet s)) + to... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (0 < consistent_classical_logic.minimum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr>) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>asks'. \<P> (bet b... | H1 x_1 x_2 x_3 \<Longrightarrow> (H2 < H3 x_1 x_2 x_3 (H4 x_4 x_5 H5)) = (\<forall>y_0\<in>H6 x_1 x_2 x_3. H7 (H8 (H9 (\<lambda>y_1. y_0 (H10 y_1)) x_4)) (H11 x_5) < H7 (H8 (H9 (\<lambda>y_2. y_0 (H10 y_2)) x_5)) (H11 x_4)) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Product_Type.Unity",
"Arbitrage_Probability_Correspondence.s... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition Unity :: unit (\\<open>'(')\\<close>... | [
"\\<lbrakk> ?H1 ?H2 (?H3 ?H2 x_1) (?H4 ?H5 ?H5 ?H5); x_1 \\<in> ?H6 ?H2 (?H3 ?H2 x_1) (?H4 ?H5 ?H5 ?H5)\\<rbrakk> \\<Longrightarrow> ?H7 (\\<lambda>y_0. ?H8 (?H9 (?H10 ?H11 y_0)) x_2 \\<le> ?H12 y_0) \\<in> ?H6 ?H2 (?H3 ?H2 x_1) (?H4 ?H5 ?H5 ?H5)"
] | 173 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.arbitrageur_maxsat | theorem (in consistent_classical_logic) arbitrageur_maxsat:
" ((k :: real) \<le> \<pi>\<^sub>m\<^sub>i\<^sub>n \<lparr> asks = asks', bids = bids' \<rparr>)
= ( MaxSAT [bet b . b \<leftarrow> bids'\<^sup>\<sim> @ asks']
\<le> total_price asks' + length bids' - total_price bids' - k )"
(is "(k \<le> \<pi>... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (k \<le> consistent_classical_logic.minimum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr>) = (real (implication_logic.relative_MaxSAT deduction implication (map bet (classical_logic.negate_bets implication f... | H1 x_1 x_2 x_3 \<Longrightarrow> (x_4 \<le> H2 x_1 x_2 x_3 (H3 x_5 x_6 H4)) = (H5 (H6 x_1 x_2 (H7 H8 (H9 (H10 x_2 x_3 x_6) x_5)) x_3) \<le> H11 (H11 (H12 (H13 x_5) (H5 (H14 x_6))) (H13 x_6)) x_4) | [
"List.length",
"Arbitrage_Probability_Correspondence.total_price",
"Groups.plus_class.plus",
"Groups.minus_class.minus",
"Arbitrage_Probability_Correspondence.classical_logic.negate_bets",
"List.append",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Probability_Inequality_C... | [
"'a list \\<Rightarrow> nat",
"'a bet_offer list \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n\\<Rightarrow> 'a \\<Rightarrow> ('a, 'b) bet_offer_scheme list\n \\<Rightarrow>... | [
"abbreviation length :: \"'a list \\<Rightarrow> nat\" where\n\"length \\<equiv> size\"",
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow... | [
"\\<lbrakk> ?H1 ?H2 ?H3 x_1 (?H4 ?H5 x_2 x_1); ?H6 (?H7 ?H8 (?H9 (?H10 ?H11 x_1 x_2) (?H10 ?H11 x_1 x_2)) (?H10 ?H11 x_1 x_2)) \\<le> x_3\\<rbrakk> \\<Longrightarrow> ?H12 (?H13 (?H14 (?H9 (?H10 ?H11 x_1 x_2) (?H10 ?H11 x_1 x_2))) x_3) (?H15 (?H9 (?H10 ?H11 x_1 x_2) (?H10 ?H11 x_1 x_2))) < ?H"
] | 191 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.arbitrageur_nonstrict_correspondence | lemma (in consistent_classical_logic) arbitrageur_nonstrict_correspondence:
" (k \<le> \<pi>\<^sub>m\<^sub>i\<^sub>n \<lparr> asks = asks', bids = bids' \<rparr>)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>asks'. \<P> (bet b)) + total_price bids' + k
\<le> (\<Sum>s\<leftarrow>bids'... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (k \<le> consistent_classical_logic.minimum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr>) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>asks'. \<P> (b... | H1 x_1 x_2 x_3 \<Longrightarrow> (x_4 \<le> H2 x_1 x_2 x_3 (H3 x_5 x_6 H4)) = (\<forall>y_0\<in>H5 x_1 x_2 x_3. H6 (H6 (H7 (H8 (\<lambda>y_1. y_0 (H9 y_1)) x_5)) (H10 x_6)) x_4 \<le> H6 (H7 (H8 (\<lambda>y_2. y_0 (H9 y_2)) x_6)) (H10 x_5)) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Product_Type.Unity",
"Arbitrage_Probability_Correspondence.s... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition Unity :: unit (\\<open>'(')\\<close>... | [
"\\<lbrakk> ?H1 ?H2; ?H3 x_1 x_2 x_3 (?H4 ?H5) \\<in> ?H6 ?H2 ?H7 (?H8 (?H9 ?H10 x_2))\\<rbrakk> \\<Longrightarrow> ?H11 ?H5 = ?H8 (?H9 ?H10 x_2)"
] | 168 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.arbitrageur_strict_correspondence | lemma (in consistent_classical_logic) arbitrageur_strict_correspondence:
" (k < \<pi>\<^sub>m\<^sub>i\<^sub>n \<lparr> asks = asks', bids = bids' \<rparr>)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>asks'. \<P> (bet b)) + total_price bids' + k
< (\<Sum>s\<leftarrow>bids'. \<P> (bet... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (k < consistent_classical_logic.minimum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr>) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>asks'. \<P> (bet b... | H1 x_1 x_2 x_3 \<Longrightarrow> (x_4 < H2 x_1 x_2 x_3 (H3 x_5 x_6 H4)) = (\<forall>y_0\<in>H5 x_1 x_2 x_3. H6 (H6 (H7 (H8 (\<lambda>y_1. y_0 (H9 y_1)) x_5)) (H10 x_6)) x_4 < H6 (H7 (H8 (\<lambda>y_2. y_0 (H9 y_2)) x_6)) (H10 x_5)) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Product_Type.Unity",
"Arbitrage_Probability_Correspondence.s... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition Unity :: unit (\\<open>'(')\\<close>... | [
"\\<lbrakk> ?H1 ?H2; ?H3 x_1 x_2 x_3 (?H4 ?H5) \\<in> ?H6 ?H2 ?H7 (?H8 (?H9 ?H10 x_2))\\<rbrakk> \\<Longrightarrow> ?H11 ?H5 = ?H8 (?H9 ?H10 x_2)"
] | 163 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.coherence_correspondence | theorem (in consistent_classical_logic) coherence_correspondence:
" (\<pi>\<^sub>m\<^sub>a\<^sub>x \<lparr> asks = asks', bids = bids' \<rparr> < 0)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>bids'. \<P> (bet b)) + total_price asks'
< (\<Sum>s\<leftarrow>asks'. \<P> (bet s)) + tota... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (consistent_classical_logic.maximum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr> < 0) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>bids'. \<P> (bet b... | H1 x_1 x_2 x_3 \<Longrightarrow> (H2 x_1 x_2 x_3 (H3 x_4 x_5 H4) < H5) = (\<forall>y_0\<in>H6 x_1 x_2 x_3. H7 (H8 (H9 (\<lambda>y_1. y_0 (H10 y_1)) x_5)) (H11 x_4) < H7 (H8 (H9 (\<lambda>y_2. y_0 (H10 y_2)) x_4)) (H11 x_5)) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Groups.zero_class.zero",
"Product_Type.Unity",
"Arbitrage_... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"class zero =\n fixes zero :: 'a (\\<open>0\\<c... | [
"\\<lbrakk> ?H1 ?H2; ?H3 ?H2 ?H4 ?H5 (?H6 ?H2 ?H7 ?H8 (?H9 ?H10 (?H11 ?H4 ?H11 ?H11 ?H4))); ?H11 ?H4 ?H11 ?H11 ?H4 = ?H11 ?H4 ?H11 ?H11 ?H4\\<rbrakk> \\<Longrightarrow> ?H12 ?H11 ?H11 ?H11 ?H4 = ?H11 ?H4 ?H11 ?H11 ?H4"
] | 185 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.coherence_maxsat | theorem (in consistent_classical_logic) coherence_maxsat:
" (\<pi>\<^sub>m\<^sub>a\<^sub>x \<lparr> asks = asks', bids = bids' \<rparr> \<le> (k :: real))
= (MaxSAT [bet b . b \<leftarrow> asks'\<^sup>\<sim> @ bids']
\<le> k - total_price asks' + total_price bids' + length asks')"
(is "(\<pi>\<^sub>m\<^... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (consistent_classical_logic.maximum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr> \<le> k) = (real (implication_logic.relative_MaxSAT deduction implication (map bet (classical_logic.negate_bets implication f... | H1 x_1 x_2 x_3 \<Longrightarrow> (H2 x_1 x_2 x_3 (H3 x_4 x_5 H4) \<le> x_6) = (H5 (H6 x_1 x_2 (H7 H8 (H9 (H10 x_2 x_3 x_4) x_5)) x_3) \<le> H11 (H11 (H12 x_6 (H13 x_4)) (H13 x_5)) (H5 (H14 x_4))) | [
"List.length",
"Arbitrage_Probability_Correspondence.total_price",
"Groups.minus_class.minus",
"Groups.plus_class.plus",
"Arbitrage_Probability_Correspondence.classical_logic.negate_bets",
"List.append",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Probability_Inequality_C... | [
"'a list \\<Rightarrow> nat",
"'a bet_offer list \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n\\<Rightarrow> 'a \\<Rightarrow> ('a, 'b) bet_offer_scheme list\n \\<Rightarrow>... | [
"abbreviation length :: \"'a list \\<Rightarrow> nat\" where\n\"length \\<equiv> size\"",
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarr... | [
"\\<lbrakk> ?H1 ?H2 ?H3 x_1 (?H4 ?H5 x_2 x_1); ?H6 (?H7 ?H8 (?H9 (?H10 ?H11 x_1 x_2) (?H10 ?H11 x_1 x_2)) (?H10 ?H11 x_1 x_2)) \\<le> x_3\\<rbrakk> \\<Longrightarrow> ?H12 (?H13 (?H14 (?H9 (?H10 ?H11 x_1 x_2) (?H10 ?H11 x_1 x_2))) x_3) (?H14 (?H10 ?H11 x_1 x_2)) \\<le> ?H12 x_3 (?H14 x_2) \\<"
] | 184 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.coherence_nonstrict_correspondence | lemma (in consistent_classical_logic) coherence_nonstrict_correspondence:
" (\<pi>\<^sub>m\<^sub>a\<^sub>x \<lparr> asks = asks', bids = bids' \<rparr> \<le> k)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>bids'. \<P> (bet b)) + total_price asks'
\<le> (\<Sum>s\<leftarrow>asks'. \<P>... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (consistent_classical_logic.maximum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr> \<le> k) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>bids'. \<P> (b... | H1 x_1 x_2 x_3 \<Longrightarrow> (H2 x_1 x_2 x_3 (H3 x_4 x_5 H4) \<le> x_6) = (\<forall>y_0\<in>H5 x_1 x_2 x_3. H6 (H7 (H8 (\<lambda>y_1. y_0 (H9 y_1)) x_5)) (H10 x_4) \<le> H6 (H6 (H7 (H8 (\<lambda>y_2. y_0 (H9 y_2)) x_4)) (H10 x_5)) x_6) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Product_Type.Unity",
"Arbitrage_Probability_Correspondence.s... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition Unity :: unit (\\<open>'(')\\<close>... | [
"\\<lbrakk> ?H1 ?H2; ?H3 x_1 x_2 x_3 (?H4 ?H5) = x_4\\<rbrakk> \\<Longrightarrow> ?H6 x_1 (\\<lambda>y_0 y_1. ?H7 (?H8 (?H9 ?H10 y_0)) (?H8 (?H9 ?H10 y_1))) x_3 \\<in> ?H6 ?H1 ?H7 (\\<lambda>y_2. ?H11 (?H3 x_1 x_2 x_3 (?H4 ?H5)))"
] | 155 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.coherence_strict_correspondence | lemma (in consistent_classical_logic) coherence_strict_correspondence:
" (\<pi>\<^sub>m\<^sub>a\<^sub>x \<lparr> asks = asks', bids = bids' \<rparr> < k)
= (\<forall> \<P> \<in> probabilities.
(\<Sum>b\<leftarrow>bids'. \<P> (bet b)) + total_price asks'
< (\<Sum>s\<leftarrow>asks'. \<P> (bet s)) +... | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> (consistent_classical_logic.maximum_payoff deduction implication falsum \<lparr>asks = asks', bids = bids'\<rparr> < k) = (\<forall>\<P> \<in>classical_logic.probabilities deduction implication falsum. (\<Sum>b\<leftarrow>bids'. \<P> (bet b... | H1 x_1 x_2 x_3 \<Longrightarrow> (H2 x_1 x_2 x_3 (H3 x_4 x_5 H4) < x_6) = (\<forall>y_0\<in>H5 x_1 x_2 x_3. H6 (H7 (H8 (\<lambda>y_1. y_0 (H9 y_1)) x_5)) (H10 x_4) < H6 (H6 (H7 (H8 (\<lambda>y_2. y_0 (H9 y_2)) x_4)) (H10 x_5)) x_6) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"Groups_List.monoid_add_class.sum_list",
"Groups.plus_class.plus",
"Probability_Logic.classical_logic.probabilities",
"Product_Type.Unity",
"Arbitrage_Probability_Correspondence.s... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"'a list \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition Unity :: unit (\\<open>'(')\\<close>... | [
"\\<lbrakk> ?H1 ?H2; ?H3 x_1 x_2 x_3 (?H4 ?H5) = x_4\\<rbrakk> \\<Longrightarrow> ?H6 x_1 (\\<lambda>y_0 y_1. ?H7 (?H8 (?H9 ?H10 y_0)) (?H8 (?H9 ?H10 y_1))) x_3 \\<in> ?H6 ?H1 ?H7 (\\<lambda>y_2. ?H11 (?H3 x_1 x_2 x_3 (?H4 ?H5)))"
] | 151 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.maximum_payoff_existence | lemma (in consistent_classical_logic) maximum_payoff_existence:
"\<exists>! x. (\<exists> p \<in> possibilities. \<pi> p bets = x)
\<and> (\<forall> q \<in> possibilities. \<pi> q bets \<le> x)" | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> \<exists>!x. (\<exists>p\<in>classical_logic.possibilities deduction implication falsum. \<pi> p bets = x) \<and> (\<forall>q\<in>classical_logic.possibilities deduction implication falsum. \<pi> q bets \<le> x) | H1 x_1 x_2 x_3 \<Longrightarrow> \<exists>!y_0. (\<exists>y_1\<in>H2 x_1 x_2 x_3. H3 y_1 x_4 = y_0) \<and> (\<forall>y_2\<in>H2 x_1 x_2 x_3. H3 y_2 x_4 \<le> y_0) | [
"Arbitrage_Probability_Correspondence.payoff",
"Arbitrage_Probability_Correspondence.classical_logic.possibilities",
"Classical_Logic.class.consistent_classical_logic"
] | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a strategy \\<Rightarrow> real",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> bool) set",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition payoff :: \"('p \\<Rightarrow> bool) \\<Rightarrow> 'p strategy \\<Rightarrow> real\" (\"\\<pi>\") where\n [simp]: \"\\<pi> s strategy \\<equiv>\n (\\<Sum> i \\<leftarrow> bids strategy. (if s (bet i) then 1 else 0) - price i)\n + (\\<Sum> i \\<leftarrow> asks strategy. price i - (if s (bet i) th... | [
"\\<lbrakk> ?H1 ?H2 x_1 x_2; ?H1 ?H2 x_1 x_2; ?H3 x_3 x_2 \\<le> ?H3 x_4 x_2\\<rbrakk> \\<Longrightarrow> ?H3 x_3 x_2 \\<le> ?H3 x_4 x_2"
] | 119 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.consistent_classical_logic.minimum_payoff_existence | lemma (in consistent_classical_logic) minimum_payoff_existence:
"\<exists>! x. (\<exists> p \<in> possibilities. \<pi> p bets = x) \<and> (\<forall> q \<in> possibilities. x \<le> \<pi> q bets)" | class.consistent_classical_logic deduction implication falsum \<Longrightarrow> \<exists>!x. (\<exists>p\<in>classical_logic.possibilities deduction implication falsum. \<pi> p bets = x) \<and> (\<forall>q\<in>classical_logic.possibilities deduction implication falsum. x \<le> \<pi> q bets) | H1 x_1 x_2 x_3 \<Longrightarrow> \<exists>!y_0. (\<exists>y_1\<in>H2 x_1 x_2 x_3. H3 y_1 x_4 = y_0) \<and> (\<forall>y_2\<in>H2 x_1 x_2 x_3. y_0 \<le> H3 y_2 x_4) | [
"Arbitrage_Probability_Correspondence.payoff",
"Arbitrage_Probability_Correspondence.classical_logic.possibilities",
"Classical_Logic.class.consistent_classical_logic"
] | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a strategy \\<Rightarrow> real",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a)\n \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> bool) set",
"('a \\<Rightarrow> bool)\n\\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarr... | [
"definition payoff :: \"('p \\<Rightarrow> bool) \\<Rightarrow> 'p strategy \\<Rightarrow> real\" (\"\\<pi>\") where\n [simp]: \"\\<pi> s strategy \\<equiv>\n (\\<Sum> i \\<leftarrow> bids strategy. (if s (bet i) then 1 else 0) - price i)\n + (\\<Sum> i \\<leftarrow> asks strategy. price i - (if s (bet i) th... | [
"\\<lbrakk> ?H1 ?H2 x_1 x_2; ?H1 ?H2 x_1 x_2; ?H3 x_3 x_2 \\<le> ?H3 x_4 x_2\\<rbrakk> \\<Longrightarrow> ?H3 x_3 x_2 \\<le> ?H3 x_4 x_2"
] | 113 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.payoff_alt_def1 | lemma payoff_alt_def1:
"\<pi> s strategy =
(\<Sum> i \<leftarrow> bids strategy. settle_bet s (bet i) - price i)
+ (\<Sum> i \<leftarrow> asks strategy. price i - settle_bet s (bet i))" | \<pi> s strategy = (\<Sum>i\<leftarrow>bids strategy. settle_bet s (bet i) - price i) + (\<Sum>i\<leftarrow>asks strategy. price i - settle_bet s (bet i)) | H1 x_1 x_2 = H2 (H3 (H4 (\<lambda>y_0. H5 (H6 x_1 (H7 y_0)) (H8 y_0)) (H9 x_2))) (H3 (H4 (\<lambda>y_1. H5 (H8 y_1) (H6 x_1 (H7 y_1))) (H10 x_2))) | [
"Arbitrage_Probability_Correspondence.strategy.asks",
"Arbitrage_Probability_Correspondence.strategy.bids",
"Arbitrage_Probability_Correspondence.bet_offer.price",
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"Arbitrage_Probability_Correspondence.settle_bet",
"Groups.minus_class.minus",
"List.l... | [
"('a, 'b) strategy_scheme \\<Rightarrow> 'a bet_offer list",
"('a, 'b) strategy_scheme \\<Rightarrow> 'a bet_offer list",
"('a, 'b) bet_offer_scheme \\<Rightarrow> real",
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a \\<Rightarrow> real",
"'a \\<Rightarrow> 'a ... | [
"definition settle_bet :: \"('p \\<Rightarrow> bool) \\<Rightarrow> 'p \\<Rightarrow> real\" where\n \"settle_bet s \\<phi> \\<equiv> if (s \\<phi>) then 1 else 0\"",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>-\\<close> 65)",
"class plus =\n fixes plus :: \"'... | [
"?H1 x_1 x_2 = ?H2 (?H3 (?H4 (?H5 (?H6 x_1)) (?H7 (?H8 x_2)))) (?H3 (?H4 (?H5 (?H6 x_1)) (?H9 x_2)))"
] | 75 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.payoff_alt_def2 | lemma payoff_alt_def2:
"\<pi> s strategy = settle s (bids strategy)
- settle s (asks strategy)
+ total_price (asks strategy)
- total_price (bids strategy)" | \<pi> s strategy = settle s (bids strategy) - settle s (asks strategy) + total_price (asks strategy) - total_price (bids strategy) | H1 x_1 x_2 = H2 (H3 (H2 (H4 x_1 (H5 x_2)) (H4 x_1 (H6 x_2))) (H7 (H6 x_2))) (H7 (H5 x_2)) | [
"Arbitrage_Probability_Correspondence.total_price",
"Arbitrage_Probability_Correspondence.strategy.asks",
"Arbitrage_Probability_Correspondence.strategy.bids",
"Arbitrage_Probability_Correspondence.settle",
"Groups.plus_class.plus",
"Groups.minus_class.minus",
"Arbitrage_Probability_Correspondence.payof... | [
"'a bet_offer list \\<Rightarrow> real",
"('a, 'b) strategy_scheme \\<Rightarrow> 'a bet_offer list",
"('a, 'b) strategy_scheme \\<Rightarrow> 'a bet_offer list",
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a bet_offer list \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> '... | [
"definition total_price :: \"('p bet_offer) list \\<Rightarrow> real\" where\n \"total_price offers \\<equiv> \\<Sum> i \\<leftarrow> offers. price i\"",
"definition settle :: \"('p \\<Rightarrow> bool) \\<Rightarrow> 'p bet_offer list \\<Rightarrow> real\" where\n \"settle s bets \\<equiv> \\<Sum> b \\<leftarr... | [
"?H1 x_1 x_2 = ?H2 (?H3 (?H4 x_1 (?H5 x_2)) (?H4 x_1 (?H6 x_2))) (?H3 (?H7 (?H5 x_2)) (?H7 (?H6 x_2)))"
] | 23 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Arbitrage_Probability_Correspondence/Arbitrage_Probability_Correspondence | Arbitrage_Probability_Correspondence.settle_alt_def | lemma settle_alt_def:
"settle q bets = length [\<phi> \<leftarrow> [ bet b . b \<leftarrow> bets ] . q \<phi>]" | settle q bets = real (length (filter q (map bet bets))) | H1 x_1 x_2 = H2 (H3 (H4 x_1 (H5 H6 x_2))) | [
"Arbitrage_Probability_Correspondence.bet_offer.bet",
"List.list.map",
"List.filter",
"List.length",
"Real.real",
"Arbitrage_Probability_Correspondence.settle"
] | [
"('a, 'b) bet_offer_scheme \\<Rightarrow> 'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a list \\<Rightarrow> 'b list",
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a list \\<Rightarrow> 'a list",
"'a list \\<Rightarrow> nat",
"nat \\<Rightarrow> real",
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a bet_offer li... | [
"primrec filter:: \"('a \\<Rightarrow> bool) \\<Rightarrow> 'a list \\<Rightarrow> 'a list\" where\n\"filter P [] = []\" |\n\"filter P (x # xs) = (if P x then x # filter P xs else filter P xs)\"",
"abbreviation length :: \"'a list \\<Rightarrow> nat\" where\n\"length \\<equiv> size\"",
"abbreviation real :: \"n... | [
"?H1 x_1 x_2 \\<le> ?H2 (?H3 (?H4 (\\<lambda>y_0. \\<not> x_1 (?H5 ?H6 y_0)) x_2))"
] | 40 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_gross_diff_eq | lemma base_gross_diff_eq:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
shows "base_gross P sqp - base_gross P sqp' =
L j * (inverse sqp - inverse (grd P (j+1))) +
sum (\<lambda> i. L i * ... | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k\<rbrakk> \<Longrightarrow> base_gross P sqp - base_gross P sqp' = L j * (inverse sqp - inverse (grd P (j + 1))) + (\<Sum>i | L i \<noteq> 0 \<and> j < i \<and> i < k. L i * (inverse (grd P i) -... | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5\<rbrakk> \<Longrightarrow> H7 (H8 x_1 x_4) (H8 x_1 x_6) = H9 (H9 (H10 (x_2 x_3) (H7 (H11 x_4) (H11 (H12 x_1 (H9 x_3 H13))))) (H14 (\<lambda>y_0. H10 (x_2 y_0) (H7 (H11 (H12 x_1 y_0)) (H11 (H12 x_1 (H9 y_0... | [
"Set.Collect",
"Groups_Big.comm_monoid_add_class.sum",
"Groups.one_class.one",
"Grid_Information.grd",
"Fields.inverse_class.inverse",
"Groups.times_class.times",
"Groups.plus_class.plus",
"Grid_Information.base_gross",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lowe... | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a set \\<Rightarrow> 'b",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow>... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\"... | [
"\\<lbrakk> ?H1 x_1; ?H2 (?H3 x_1) (?H4 x_1) = ?H5 x_1; ?H6 < ?H7 (?H8 x_1 (?H9 (?H10 (?H11 (?H12 x_1)) (?H12 x_1)) (?H13 x_1))) (?H14 (?H12 x_1) (?H15 (\\<lambda>y_0. ?H16 < ?H12 x_1 y_0)))\\<rbrakk> \\<Longrightarrow> ?H17 (?H12 x_1) (?H15 (\\<lambda>y_1. ?H16 < ?H12 x_1 y_1)) \\<le> ?H18 (?H12 x_1) x_"
] | 288 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_gross_diff_eq' | lemma base_gross_diff_eq':
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "j = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "base_gross P sqp - base_gross P sqp' = L j * (inverse sqp - inverse sqp')" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; j = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> base_gross P sqp - base_gross P sqp' = L j * (inverse sqp - inverse sqp') | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_3 = H5 x_1 x_5; H6 < x_4; x_4 \<le> x_5\<rbrakk> \<Longrightarrow> H7 (H8 x_1 x_4) (H8 x_1 x_5) = H9 (x_2 x_3) (H7 (H10 x_4) (H10 x_5)) | [
"Fields.inverse_class.inverse",
"Groups.times_class.times",
"Grid_Information.base_gross",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rig... | [
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"definition base_gross where\n\"base_gross P = gen_base (grd P) (gross_fct (lq P) (fee P))\"",
"class minus =\n fixes m... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H3 x_1; ?H4 x_1 = ?H5 x_1; ?H6 x_1 x_4 \\<noteq> ?H7\\<rbrakk> \\<Longrightarrow> ?H8 (?H9 x_1 x_4) (?H10 (?H11 (x_2 (?H6 x_1 x_4))) (x_3 (?H6 x_1 x_4))) \\<le> ?H11 (?H9 x_1 x_4)"
] | 99 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_gross_sum | lemma base_gross_sum:
assumes "clmm_dsc P"
and "0 < sqp"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
shows "base_gross P sqp =
L j * (inverse sqp - inverse (grd P (j+1))) +
sum (\<lambda>i. L i * (inverse (grd P i) - inverse (grd P (i+1))))
{i. L i \<noteq> 0 \<and> j < i}" | \<lbrakk>clmm_dsc P; 0 < sqp; L = gross_fct (lq P) (fee P); j = lower_tick P sqp\<rbrakk> \<Longrightarrow> base_gross P sqp = L j * (inverse sqp - inverse (grd P (j + 1))) + (\<Sum>i | L i \<noteq> 0 \<and> j < i. L i * (inverse (grd P i) - inverse (grd P (i + 1)))) | \<lbrakk>H1 x_1; H2 < x_2; x_3 = H3 (H4 x_1) (H5 x_1); x_4 = H6 x_1 x_2\<rbrakk> \<Longrightarrow> H7 x_1 x_2 = H8 (H9 (x_3 x_4) (H10 (H11 x_2) (H11 (H12 x_1 (H8 x_4 H13))))) (H14 (\<lambda>y_0. H9 (x_3 y_0) (H10 (H11 (H12 x_1 y_0)) (H11 (H12 x_1 (H8 y_0 H13))))) (H15 (\<lambda>y_1. x_3 y_1 \<noteq> H2 \<and> x_4 < y_1... | [
"Set.Collect",
"Groups_Big.comm_monoid_add_class.sum",
"Groups.one_class.one",
"Grid_Information.grd",
"Fields.inverse_class.inverse",
"Groups.minus_class.minus",
"Groups.times_class.times",
"Groups.plus_class.plus",
"Grid_Information.base_gross",
"CLMM_Description.lower_tick",
"Grid_Information... | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a set \\<Rightarrow> 'b",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow>... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\"... | [
"\\<lbrakk> ?H1 x_1; ?H2 < x_2; ?H3 (?H4 x_1) (?H5 x_1) x_2 = ?H2; ?H6 x_1 x_2 = ?H2; ?H7 x_1 x_2 = ?H2; ?H8 x_1 x_2 = ?H9 (?H10 (?H11 (?H12 x_1 x_2)) (?H13)) (?H14 (\\<lambda>y_0. ?H11 (?H12 x_1 y_0)) (?H15 (\\<lambda>y_1. ?H2 < y_1 \\<and> y_1 \\<le> x_2)))\\<rbrakk> \\<Longrightarrow> ?H16 x_2 = ?H11"
] | 174 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_le_quote_gross | lemma base_le_quote_gross:
assumes "clmm_dsc P'"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "base_gross P' sqp - base_gross P' sqp' \<le>
(quote_gross P' sqp' - quote_gross P' sqp)/(sqp * sqp)" | \<lbrakk>clmm_dsc P'; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> base_gross P' sqp - base_gross P' sqp' \<le> (quote_gross P' sqp' - quote_gross P' sqp) / (sqp * sqp) | \<lbrakk>H1 x_1; H2 < x_2; x_2 \<le> x_3\<rbrakk> \<Longrightarrow> H3 (H4 x_1 x_2) (H4 x_1 x_3) \<le> H5 (H3 (H6 x_1 x_3) (H6 x_1 x_2)) (H7 x_2 x_2) | [
"Groups.times_class.times",
"Grid_Information.quote_gross",
"Fields.inverse_class.inverse_divide",
"Grid_Information.base_gross",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.clmm_dsc"
] | [
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<R... | [
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"definition base_gross... | [
"\\<lbrakk> ?H1 x_1; ?H2 < x_2\\<rbrakk> \\<Longrightarrow> ?H3 (?H4 x_1 x_2) (?H5 (?H6 x_1 x_2) x_2) \\<le> ?H7 (?H4 x_1 x_2) x_2"
] | 62 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_diff_eq | lemma base_net_diff_eq:
assumes "clmm_dsc P"
and "L = lq P"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
shows "base_net P sqp - base_net P sqp' =
L j * (inverse sqp - inverse (grd P (j+1))) +
sum (\<lambda> i. L i * (inverse (grd P i) - inver... | \<lbrakk>clmm_dsc P; L = lq P; j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k\<rbrakk> \<Longrightarrow> base_net P sqp - base_net P sqp' = L j * (inverse sqp - inverse (grd P (j + 1))) + (\<Sum>i | L i \<noteq> 0 \<and> j < i \<and> i < k. L i * (inverse (grd P i) - inverse (grd P (i + 1))... | \<lbrakk>H1 x_1; x_2 = H2 x_1; x_3 = H3 x_1 x_4; x_5 = H3 x_1 x_6; H4 < x_4; x_4 \<le> x_6; x_3 < x_5\<rbrakk> \<Longrightarrow> H5 (H6 x_1 x_4) (H6 x_1 x_6) = H7 (H7 (H8 (x_2 x_3) (H5 (H9 x_4) (H9 (H10 x_1 (H7 x_3 H11))))) (H12 (\<lambda>y_0. H8 (x_2 y_0) (H5 (H9 (H10 x_1 y_0)) (H9 (H10 x_1 (H7 y_0 H11))))) (H13 (\<la... | [
"Set.Collect",
"Groups_Big.comm_monoid_add_class.sum",
"Groups.one_class.one",
"Grid_Information.grd",
"Fields.inverse_class.inverse",
"Groups.times_class.times",
"Groups.plus_class.plus",
"Grid_Information.base_net",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lower_... | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a set \\<Rightarrow> 'b",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow>... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\"... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 \\<le> x_3; ?H3 x_1 x_3 \\<le> x_2; ?H4 < x_3; ?H5 (?H6 x_1 (?H7 (?H8 (?H9 (?H10 x_1 x_2)) (?H10 x_1 x_3)) (?H11)) x_4) ?H12 \\<le> x_5\\<rbrakk> \\<Longrightarrow> ?H13 (\\<lambda>y_0. ?H14 (\\<lambda>y_1. ?H15 (\\<lambda>y_2. y_2 = y_1 \\<and> ?H3 x_1 y_2 = x_2) y_0) y_0)"
] | 271 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_diff_eq' | lemma base_net_diff_eq':
assumes "clmm_dsc P"
and "L = lq P"
and "j = lower_tick P sqp"
and "j = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "base_net P sqp - base_net P sqp' = L j * (inverse sqp - inverse sqp')" | \<lbrakk>clmm_dsc P; L = lq P; j = lower_tick P sqp; j = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> base_net P sqp - base_net P sqp' = L j * (inverse sqp - inverse sqp') | \<lbrakk>H1 x_1; x_2 = H2 x_1; x_3 = H3 x_1 x_4; x_3 = H3 x_1 x_5; H4 < x_4; x_4 \<le> x_5\<rbrakk> \<Longrightarrow> H5 (H6 x_1 x_4) (H6 x_1 x_5) = H7 (x_2 x_3) (H5 (H8 x_4) (H8 x_5)) | [
"Fields.inverse_class.inverse",
"Groups.times_class.times",
"Grid_Information.base_net",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.lq",
"CLMM_Description.clmm_dsc"
] | [
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rig... | [
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"class minus =\n fixes minus :: \"'a \\<Rightarr... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 = ?H3 x_1 x_3; ?H4 < x_3\\<rbrakk> \\<Longrightarrow> ?H5 (?H6 x_1 x_3) (?H2 x_1 x_2) \\<le> ?H7 (?H8 (?H6 x_1 x_3) (?H9 (?H6 x_1 x_2))) (?H2 x_1 x_2)"
] | 86 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_eq_only_if | lemma base_net_eq_only_if:
assumes "clmm_dsc P"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
and "quote_gross P sqp' = quote_gross P sqp"
shows "base_net P sqp' = base_net P sqp" | \<lbrakk>clmm_dsc P; j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k; quote_gross P sqp' = quote_gross P sqp\<rbrakk> \<Longrightarrow> base_net P sqp' = base_net P sqp | \<lbrakk>H1 x_1; x_2 = H2 x_1 x_3; x_4 = H2 x_1 x_5; H3 < x_3; x_3 \<le> x_5; x_2 < x_4; H4 x_1 x_5 = H4 x_1 x_3\<rbrakk> \<Longrightarrow> H5 x_1 x_5 = H5 x_1 x_3 | [
"Grid_Information.base_net",
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarro... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P prc)\"",
"defin... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 = ?H3\\<rbrakk> \\<Longrightarrow> ?H4 x_1 x_2 = ?H5 x_1 x_2"
] | 86 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_eq_only_if' | lemma base_net_eq_only_if':
assumes "clmm_dsc P"
and "L = lq P"
and "j = lower_tick P sqp"
and "j = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "quote_gross P sqp = quote_gross P sqp'"
shows "base_net P sqp = base_net P sqp'" | \<lbrakk>clmm_dsc P; L = lq P; j = lower_tick P sqp; j = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; quote_gross P sqp = quote_gross P sqp'\<rbrakk> \<Longrightarrow> base_net P sqp = base_net P sqp' | \<lbrakk>H1 x_1; x_2 = H2 x_1; x_3 = H3 x_1 x_4; x_3 = H3 x_1 x_5; H4 < x_4; x_4 \<le> x_5; H5 x_1 x_4 = H5 x_1 x_5\<rbrakk> \<Longrightarrow> H6 x_1 x_4 = H6 x_1 x_5 | [
"Grid_Information.base_net",
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.lq",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarro... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P prc)\"",
"defin... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 (?H3 x_1 x_2) = ?H4\\<rbrakk> \\<Longrightarrow> ?H5 x_1 x_2 = ?H6 x_1 x_2 \\<and> ?H7 x_1 x_2 = ?H4"
] | 93 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_grd_min_le | lemma base_net_grd_min_le:
assumes "clmm_dsc P"
and "sqp \<le> grd_min P"
and "0 < sqp"
shows "base_net P sqp = base_net P (grd_min P)" | \<lbrakk>clmm_dsc P; sqp \<le> grd_min P; 0 < sqp\<rbrakk> \<Longrightarrow> base_net P sqp = base_net P (grd_min P) | \<lbrakk>H1 x_1; x_2 \<le> H2 x_1; H3 < x_2\<rbrakk> \<Longrightarrow> H4 x_1 x_2 = H4 x_1 (H2 x_1) | [
"Grid_Information.base_net",
"Groups.zero_class.zero",
"Grid_Information.grd_min",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition grd_min where\n \"grd_min P = idx_min_img (grd P) (lq P)\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 = ?H3\\<rbrakk> \\<Longrightarrow> ?H4 x_1 = ?H3"
] | 39 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_grd_min_lt | lemma base_net_grd_min_lt:
assumes "clmm_dsc P"
and "sqp < grd_min P"
and "0 < sqp"
shows "base_net P sqp = base_net P (grd_min P)" | \<lbrakk>clmm_dsc P; sqp < grd_min P; 0 < sqp\<rbrakk> \<Longrightarrow> base_net P sqp = base_net P (grd_min P) | \<lbrakk>H1 x_1; x_2 < H2 x_1; H3 < x_2\<rbrakk> \<Longrightarrow> H4 x_1 x_2 = H4 x_1 (H2 x_1) | [
"Grid_Information.base_net",
"Groups.zero_class.zero",
"Grid_Information.grd_min",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition grd_min where\n \"grd_min P = idx_min_img (grd P) (lq P)\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 = ?H3\\<rbrakk> \\<Longrightarrow> ?H4 x_1 = ?H3"
] | 35 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_quote_lbound | lemma base_net_quote_lbound:
assumes "clmm_dsc P'"
and "\<And>i. fee P' i = phi"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "(1 - phi) * (quote_gross P' sqp' - quote_gross P' sqp)/(sqp' * sqp') \<le>
base_net P' sqp - base_net P' sqp'" | \<lbrakk>clmm_dsc P'; \<And>i. fee P' i = phi; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> (1 - phi) * (quote_gross P' sqp' - quote_gross P' sqp) / (sqp' * sqp') \<le> base_net P' sqp - base_net P' sqp' | \<lbrakk>H1 x_1; \<And>y_0. H2 x_1 y_0 = x_2; H3 < x_3; x_3 \<le> x_4\<rbrakk> \<Longrightarrow> H4 (H5 (H6 H7 x_2) (H6 (H8 x_1 x_4) (H8 x_1 x_3))) (H5 x_4 x_4) \<le> H6 (H9 x_1 x_3) (H9 x_1 x_4) | [
"Grid_Information.base_net",
"Grid_Information.quote_gross",
"Groups.one_class.one",
"Groups.minus_class.minus",
"Groups.times_class.times",
"Fields.inverse_class.inverse_divide",
"Groups.zero_class.zero",
"Grid_Information.fee",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"'a \\<Rightarrow>... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 = ?H3\\<rbrakk> \\<Longrightarrow> ?H4 (?H5 (?H6 ?H7 (?H2 x_1 x_2)) (?H8 x_1 x_2)) (?H9 x_1 x_2) \\<le> ?H7"
] | 91 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_quote_ubound | lemma base_net_quote_ubound:
assumes "clmm_dsc P'"
and "\<And>i. fee P' i = phi"
and "phi < 1"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "base_net P' sqp - base_net P' sqp' \<le>
(1 - phi) * (quote_gross P' sqp' - quote_gross P' sqp)/(sqp * sqp)" | \<lbrakk>clmm_dsc P'; \<And>i. fee P' i = phi; phi < 1; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> base_net P' sqp - base_net P' sqp' \<le> (1 - phi) * (quote_gross P' sqp' - quote_gross P' sqp) / (sqp * sqp) | \<lbrakk>H1 x_1; \<And>y_0. H2 x_1 y_0 = x_2; x_2 < H3; H4 < x_3; x_3 \<le> x_4\<rbrakk> \<Longrightarrow> H5 (H6 x_1 x_3) (H6 x_1 x_4) \<le> H7 (H8 (H5 H3 x_2) (H5 (H9 x_1 x_4) (H9 x_1 x_3))) (H8 x_3 x_3) | [
"Grid_Information.quote_gross",
"Groups.times_class.times",
"Fields.inverse_class.inverse_divide",
"Grid_Information.base_net",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"Groups.one_class.one",
"Grid_Information.fee",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<R... | [
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"definition base_net w... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 = ?H3; ?H4 \\<le> x_3; x_3 \\<le> ?H5 ?H3 x_4; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3; ?H2 x_1 x_2 = ?H3;"
] | 160 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.base_net_sum | lemma base_net_sum:
assumes "clmm_dsc P"
and "0 < sqp"
and "L = lq P"
and "j = lower_tick P sqp"
shows "base_net P sqp =
L j * (inverse sqp - inverse (grd P (j+1))) +
sum (\<lambda>i. L i * (inverse (grd P i) - inverse (grd P (i+1))))
{i. L i \<noteq> 0 \<and> j < i}" | \<lbrakk>clmm_dsc P; 0 < sqp; L = lq P; j = lower_tick P sqp\<rbrakk> \<Longrightarrow> base_net P sqp = L j * (inverse sqp - inverse (grd P (j + 1))) + (\<Sum>i | L i \<noteq> 0 \<and> j < i. L i * (inverse (grd P i) - inverse (grd P (i + 1)))) | \<lbrakk>H1 x_1; H2 < x_2; x_3 = H3 x_1; x_4 = H4 x_1 x_2\<rbrakk> \<Longrightarrow> H5 x_1 x_2 = H6 (H7 (x_3 x_4) (H8 (H9 x_2) (H9 (H10 x_1 (H6 x_4 H11))))) (H12 (\<lambda>y_0. H7 (x_3 y_0) (H8 (H9 (H10 x_1 y_0)) (H9 (H10 x_1 (H6 y_0 H11))))) (H13 (\<lambda>y_1. x_3 y_1 \<noteq> H2 \<and> x_4 < y_1))) | [
"Set.Collect",
"Groups_Big.comm_monoid_add_class.sum",
"Groups.one_class.one",
"Grid_Information.grd",
"Fields.inverse_class.inverse",
"Groups.minus_class.minus",
"Groups.times_class.times",
"Groups.plus_class.plus",
"Grid_Information.base_net",
"CLMM_Description.lower_tick",
"Grid_Information.l... | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a set \\<Rightarrow> 'b",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a \\<Rightarrow> 'a",
"'a \\<Rightarrow>... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class inverse = divide +\n fixes inverse :: \"'a \\<Rightarrow> 'a\"\nbegin",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\"... | [
"\\<lbrakk> ?H1 x_1; ?H2 < x_2; ?H3 x_1 x_2 \\<le> ?H4 x_1 x_3; ?H5 x_1 x_3 \\<le> x_2\\<rbrakk> \\<Longrightarrow> ?H6 (?H7 (?H8 (?H9 (?H10 x_1 x_2)) (?H10 x_1 x_2)) (?H11 (?H3 x_1 x_2))) (?H12 (\\<lambda>y_0. ?H11 (?H3 x_1 y_0)) (?H13 (\\<lambda>y_1. ?H2 < y_1 \\<and> y_1 \\<le> x_2))) \\<le> ?H3 x_1 x_2"
] | 162 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_base_gross_antimono | lemma clmm_base_gross_antimono:
assumes "clmm_dsc P"
shows "antimono (base_gross P)" | clmm_dsc P \<Longrightarrow> antimono_on UNIV (base_gross P) | H1 x_1 \<Longrightarrow> H2 H3 (H4 x_1) | [
"Grid_Information.base_gross",
"Set.UNIV",
"Fun.ord_class.antimono_on",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a set",
"'a set \\<Rightarrow> ('a \\<Rightarrow> 'b) \\<Rightarrow> bool",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightar... | [
"definition base_gross where\n\"base_gross P = gen_base (grd P) (gross_fct (lq P) (fee P))\"",
"abbreviation UNIV :: \"'a set\"\n where \"UNIV \\<equiv> top\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n ... | [
"?H1 x_1 \\<Longrightarrow> ?H2 ?H3 (?H4 x_1)"
] | 4 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_base_gross_grd_max | lemma clmm_base_gross_grd_max:
assumes "clmm_dsc P"
and "nz_support (lq P) \<noteq> {}"
shows "base_gross P (grd_max P) = 0" | \<lbrakk>clmm_dsc P; nz_support (lq P) \<noteq> {}\<rbrakk> \<Longrightarrow> base_gross P (grd_max P) = 0 | \<lbrakk>H1 x_1; H2 (H3 x_1) \<noteq> H4\<rbrakk> \<Longrightarrow> H5 x_1 (H6 x_1) = H7 | [
"Groups.zero_class.zero",
"Grid_Information.grd_max",
"Grid_Information.base_gross",
"Set.empty",
"Grid_Information.lq",
"CLMM_Misc.nz_support",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a set",
"(int \\<Rightarrow> real)... | [
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition grd_max where\n \"grd_max P = idx_max_img (grd P) (lq P)\"",
"definition base_gross where\n\"base_gross P = gen_base (grd P) (gross_fct (lq P) (fee P))\"",
"abbreviation empty :: \"'a set\" (\\<open>{}\\<close>)\n where \"{} \\<equiv> bot... | [
"\\<lbrakk> ?H1 x_1; ?H2 (?H3 x_1) \\<noteq> ?H4\\<rbrakk> \\<Longrightarrow> ?H5 x_1 (?H6 x_1) \\<le> ?H7 x_1 \\<and> ?H8 \\<le> ?H5 x_1 (?H6 x_1)"
] | 52 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_base_net_antimono | lemma clmm_base_net_antimono:
assumes "clmm_dsc P"
shows "antimono (base_net P)" | clmm_dsc P \<Longrightarrow> antimono_on UNIV (base_net P) | H1 x_1 \<Longrightarrow> H2 H3 (H4 x_1) | [
"Grid_Information.base_net",
"Set.UNIV",
"Fun.ord_class.antimono_on",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a set",
"'a set \\<Rightarrow> ('a \\<Rightarrow> 'b) \\<Rightarrow> bool",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightar... | [
"definition base_net where\n\"base_net P = gen_base (grd P) (lq P)\"",
"abbreviation UNIV :: \"'a set\"\n where \"UNIV \\<equiv> top\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> ... | [
"?H1 x_1 \\<Longrightarrow> ?H2 ?H3 (?H4 x_1)"
] | 4 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dscI | lemma clmm_dscI[intro]:
assumes "span_grid P"
and "finite_liq P"
and "\<forall>i. 0 \<le> lq P i"
and "\<forall>i. 0 \<le> fee P i"
and "\<forall>i. fee P i < 1"
shows "clmm_dsc P" | \<lbrakk>span_grid P; finite_liq P; \<forall>i. 0 \<le> lq P i; \<forall>i. 0 \<le> fee P i; \<forall>i. fee P i < 1\<rbrakk> \<Longrightarrow> clmm_dsc P | \<lbrakk>H1 x_1; H2 x_1; \<forall>y_0. H3 \<le> H4 x_1 y_0; \<forall>y_1. H3 \<le> H5 x_1 y_1; \<forall>y_2. H5 x_1 y_2 < H6\<rbrakk> \<Longrightarrow> H7 x_1 | [
"CLMM_Description.clmm_dsc",
"Groups.one_class.one",
"Grid_Information.fee",
"Grid_Information.lq",
"Groups.zero_class.zero",
"Grid_Information.finite_liq",
"Grid_Information.span_grid"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(... | [
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < 1)\"",
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition fee::\"grid_info \\<R... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1; \\<forall>y_0. ?H3 < ?H4 x_1 y_0; \\<forall>y_1. ?H3 < ?H5 x_1 y_1; \\<forall>y_2. ?H6 x_1 y_2 < ?H7\\<rbrakk> \\<Longrightarrow> ?H8 x_1"
] | 21 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_fees | lemma clmm_dsc_fees:
assumes "clmm_dsc P"
shows "(\<forall>i. 0 \<le> fee P i) \<and> (\<forall>i. fee P i < 1)" | clmm_dsc P \<Longrightarrow> (\<forall>i. 0 \<le> fee P i) \<and> (\<forall>i. fee P i < 1) | H1 x_1 \<Longrightarrow> (\<forall>y_0. H2 \<le> H3 x_1 y_0) \<and> (\<forall>y_1. H3 x_1 y_1 < H4) | [
"Groups.one_class.one",
"Grid_Information.fee",
"Groups.zero_class.zero",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"fee P = snd (snd P)\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (fini... | [
"\\<lbrakk> ?H1 x_1; ?H2 \\<le> x_2\\<rbrakk> \\<Longrightarrow> ?H3 x_1 x_2 \\<le> ?H4"
] | 70 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_fees_neq_1 | lemma clmm_dsc_fees_neq_1:
assumes "clmm_dsc P"
shows "\<forall>i. fee P i \<noteq> 1" | clmm_dsc P \<Longrightarrow> \<forall>i. fee P i \<noteq> 1 | H1 x_1 \<Longrightarrow> \<forall>y_0. H2 x_1 y_0 \<noteq> H3 | [
"Groups.one_class.one",
"Grid_Information.fee",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"fee P = snd (snd P)\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n ... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1 = (\\<lambda>y_0. ?H3)"
] | 31 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grd_Suc | lemma clmm_dsc_grd_Suc:
assumes "clmm_dsc P"
shows "grd P i < grd P (i+1)" | clmm_dsc P \<Longrightarrow> grd P i < grd P (i + 1) | H1 x_1 \<Longrightarrow> H2 x_1 x_2 < H2 x_1 (H3 x_2 H4) | [
"Groups.one_class.one",
"Groups.plus_class.plus",
"Grid_Information.grd",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"class plus =\n fixes plus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>+\\<close> 65)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<lon... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1 x_2 = ?H3 (?H2 x_1 x_2) ?H4"
] | 15 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grd_mono | lemma clmm_dsc_grd_mono:
assumes "clmm_dsc P"
and "i \<le> j"
shows "grd P i \<le> grd P j" | \<lbrakk>clmm_dsc P; i \<le> j\<rbrakk> \<Longrightarrow> grd P i \<le> grd P j | \<lbrakk>H1 x_1; x_2 \<le> x_3\<rbrakk> \<Longrightarrow> H2 x_1 x_2 \<le> H2 x_1 x_3 | [
"Grid_Information.grd",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < 1... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1 = ?H2 x_2"
] | 48 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grd_smono | lemma clmm_dsc_grd_smono:
assumes "clmm_dsc P"
and "i < j"
shows "grd P i < grd P j" | \<lbrakk>clmm_dsc P; i < j\<rbrakk> \<Longrightarrow> grd P i < grd P j | \<lbrakk>H1 x_1; x_2 < x_3\<rbrakk> \<Longrightarrow> H2 x_1 x_2 < H2 x_1 x_3 | [
"Grid_Information.grd",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < 1... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1 = ?H2 x_2"
] | 40 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grid(1) | lemma clmm_dsc_grid[simp]:
assumes "clmm_dsc P"
shows "strict_mono (grd P)" "(\<forall>i. 0 < grd P i)"
"(\<forall>r>0. \<exists>i. grd P i < r)" "(\<forall>r. \<exists>i. r < grd P i)" | clmm_dsc P \<Longrightarrow> strict_mono (grd P) | H1 x_1 \<Longrightarrow> H2 (H3 x_1) | [
"Grid_Information.grd",
"Fun.order_class.strict_mono",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"('a \\<Rightarrow> 'b) \\<Rightarrow> bool",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < 1... | [
"?H1 x_1 \\<Longrightarrow> ?H2 (?H3 x_1)"
] | 3 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grid(2) | lemma clmm_dsc_grid[simp]:
assumes "clmm_dsc P"
shows "strict_mono (grd P)" "(\<forall>i. 0 < grd P i)"
"(\<forall>r>0. \<exists>i. grd P i < r)" "(\<forall>r. \<exists>i. r < grd P i)" | clmm_dsc P \<Longrightarrow> \<forall>i. 0 < grd P i | H1 x_1 \<Longrightarrow> \<forall>y_0. H2 < H3 x_1 y_0 | [
"Grid_Information.grd",
"Groups.zero_class.zero",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<f... | [
"?H1 x_1 \\<Longrightarrow> ?H2 \\<le> ?H3 x_1 x_2"
] | 19 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grid(3) | lemma clmm_dsc_grid[simp]:
assumes "clmm_dsc P"
shows "strict_mono (grd P)" "(\<forall>i. 0 < grd P i)"
"(\<forall>r>0. \<exists>i. grd P i < r)" "(\<forall>r. \<exists>i. r < grd P i)" | clmm_dsc P \<Longrightarrow> \<forall>r>0. \<exists>i. grd P i < r | H1 x_1 \<Longrightarrow> \<forall>y_0>H2. \<exists>y_1. H3 x_1 y_1 < y_0 | [
"Grid_Information.grd",
"Groups.zero_class.zero",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<f... | [
"?H1 x_1 \\<Longrightarrow> ?H2 \\<le> ?H3 x_1 x_2"
] | 34 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_grid(4) | lemma clmm_dsc_grid[simp]:
assumes "clmm_dsc P"
shows "strict_mono (grd P)" "(\<forall>i. 0 < grd P i)"
"(\<forall>r>0. \<exists>i. grd P i < r)" "(\<forall>r. \<exists>i. r < grd P i)" | clmm_dsc P \<Longrightarrow> \<forall>r. \<exists>i. r < grd P i | H1 x_1 \<Longrightarrow> \<forall>y_0. \<exists>y_1. y_0 < H2 x_1 y_1 | [
"Grid_Information.grd",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < 1... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1 = ?H2 x_2"
] | 34 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_gross_liq | lemma clmm_dsc_gross_liq:
assumes "clmm_dsc P"
shows "nz_support (gross_fct (lq P) (fee P)) = nz_support (lq P)" | clmm_dsc P \<Longrightarrow> nz_support (gross_fct (lq P) (fee P)) = nz_support (lq P) | H1 x_1 \<Longrightarrow> H2 (H3 (H4 x_1) (H5 x_1)) = H2 (H4 x_1) | [
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Misc.nz_support",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real)\n... | [
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"fee P = snd (snd P)\"",
"definition lq::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"lq P = fst (snd P)\"",
"definition gross_fct where\n\"gross_fct f phi = (\\<lambda>i. f i / (one_cpl phi i))\"",
"definition nz... | [
"\\<lbrakk> ?H1 x_1; x_2 \\<in> ?H2 ?H3\\<rbrakk> \\<Longrightarrow> ?H4 x_1 x_2 \\<in> ?H2 ?H3 \\<and> ?H5 x_1 x_2 \\<in> ?H2 ?H3 \\<and> ?H4 x_1 x_2 = ?H5 x_1 x_2 \\<and> ?H5 x_1 x_2 < ?H4 x_1 x_2 \\<and> ?H5 x_1 x_2 \\<le> ?H4 x_1 x_2"
] | 170 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_gross_liq_zero_iff | lemma clmm_dsc_gross_liq_zero_iff:
assumes "clmm_dsc P"
shows "(lq P i = 0) \<longleftrightarrow> (gross_fct (lq P) (fee P) i = 0)" | clmm_dsc P \<Longrightarrow> (lq P i = 0) = (gross_fct (lq P) (fee P) i = 0) | H1 x_1 \<Longrightarrow> (H2 x_1 x_2 = H3) = (H4 (H2 x_1) (H5 x_1) x_2 = H3) | [
"Grid_Information.fee",
"CLMM_Misc.gross_fct",
"Groups.zero_class.zero",
"Grid_Information.lq",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real)\n\\<Rightarrow> (int \\<Rightarrow> real) \\<Rightarrow> int \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Righta... | [
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"fee P = snd (snd P)\"",
"definition gross_fct where\n\"gross_fct f phi = (\\<lambda>i. f i / (one_cpl phi i))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lq::\"grid_info \\<Rightarrow> (int\\<Rightarr... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_1 x_2 = ?H3\\<rbrakk> \\<Longrightarrow> ?H4 ?H5 x_1 x_2 = ?H6 x_1"
] | 63 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_liq(1) | lemma clmm_dsc_liq:
assumes "clmm_dsc P"
shows "finite_liq P" "0 \<le> lq P i" | clmm_dsc P \<Longrightarrow> finite_liq P | H1 x_1 \<Longrightarrow> H2 x_1 | [
"Grid_Information.finite_liq",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition finite_liq where\n\"finite_liq P \\<longleftrightarrow> finite (nz_support (lq P))\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (\\<forall>i. 0 \\<le> fee P i) \\<and> (\\<forall>i. fee P i < ... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1"
] | 2 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_liq(2) | lemma clmm_dsc_liq:
assumes "clmm_dsc P"
shows "finite_liq P" "0 \<le> lq P i" | clmm_dsc P \<Longrightarrow> 0 \<le> lq P i | H1 x_1 \<Longrightarrow> H2 \<le> H3 x_1 x_2 | [
"Grid_Information.lq",
"Groups.zero_class.zero",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition lq::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"lq P = fst (snd P)\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and> (finite_liq P) \\<and> (\\<forall>i. 0 \\<le> lq P i) \\<and>\n (... | [
"?H1 x_1 \\<Longrightarrow> ?H2 \\<le> ?H3 x_1 x_2"
] | 3 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_dsc_span_grid | lemma clmm_dsc_span_grid:
assumes "clmm_dsc P"
shows "span_grid P" | clmm_dsc P \<Longrightarrow> span_grid P | H1 x_1 \<Longrightarrow> H2 x_1 | [
"Grid_Information.span_grid",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> bool"
] | [
"definition span_grid where\n\"span_grid P \\<longleftrightarrow> strict_mono (grd P) \\<and> (\\<forall>i. 0 < grd P i) \\<and>\n (\\<forall>r>0. \\<exists>i. grd P i < r) \\<and> (\\<forall> r. \\<exists>i. r < grd P i)\"",
"definition clmm_dsc where\n\"clmm_dsc P \\<longleftrightarrow> (span_grid P) \\<and>... | [
"?H1 x_1 \\<Longrightarrow> ?H2 x_1"
] | 2 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_gen_quote_grd_min | lemma clmm_gen_quote_grd_min:
assumes "clmm_dsc P"
and "nz_support L \<noteq> {}"
and "finite (nz_support L)"
and "nz_support L = nz_support (lq P)"
shows "gen_quote (grd P) L (grd_min P) = 0" | \<lbrakk>clmm_dsc P; nz_support L \<noteq> {}; finite (nz_support L); nz_support L = nz_support (lq P)\<rbrakk> \<Longrightarrow> gen_quote (grd P) L (grd_min P) = 0 | \<lbrakk>H1 x_1; H2 x_2 \<noteq> H3; H4 (H2 x_2); H2 x_2 = H2 (H5 x_1)\<rbrakk> \<Longrightarrow> H6 (H7 x_1) x_2 (H8 x_1) = H9 | [
"Groups.zero_class.zero",
"Grid_Information.grd_min",
"Grid_Information.grd",
"Grid_Information.gen_quote",
"Grid_Information.lq",
"Finite_Set.finite",
"Set.empty",
"CLMM_Misc.nz_support",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real)\n\\<Rightarr... | [
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition grd_min where\n \"grd_min P = idx_min_img (grd P) (lq P)\"",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition gen_quote where\n\"gen_quote = (\\<lambda> gamma L pi. gen_token (ga... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 \\<noteq> ?H3; ?H4 (?H2 x_2)\\<rbrakk> \\<Longrightarrow> ?H5 x_1 x_3 = ?H6 (?H7 x_1) (\\<lambda>y_0. if y_0 \\<in> ?H2 x_2 then ?H8 x_1 y_0 else ?H9) (?H7 x_1 x_3) \\<and> ?H10 \\<le> ?H5 x_1 x_3"
] | 125 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_diff_eq | lemma clmm_quote_gross_diff_eq:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
shows "quote_gross P sqp' - quote_gross P sqp = L k * (sqp' - grd P k) +
sum (\<lambda> i. L i * (grd P (i+1) - g... | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k\<rbrakk> \<Longrightarrow> quote_gross P sqp' - quote_gross P sqp = L k * (sqp' - grd P k) + (\<Sum>i | L i \<noteq> 0 \<and> j < i \<and> i < k. L i * (grd P (i + 1) - grd P i)) + L j * (grd P... | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5\<rbrakk> \<Longrightarrow> H7 (H8 x_1 x_6) (H8 x_1 x_4) = H9 (H9 (H10 (x_2 x_5) (H7 x_6 (H11 x_1 x_5))) (H12 (\<lambda>y_0. H10 (x_2 y_0) (H7 (H11 x_1 (H9 y_0 H13)) (H11 x_1 y_0))) (H14 (\<lambda>y_1. x_2... | [
"Set.Collect",
"Groups.one_class.one",
"Groups_Big.comm_monoid_add_class.sum",
"Grid_Information.grd",
"Groups.times_class.times",
"Groups.plus_class.plus",
"Grid_Information.quote_gross",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee"... | [
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"'a",
"('a \\<Rightarrow> 'b) \\<Rightarrow> 'a set \\<Rightarrow> 'b",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
... | [
"class one =\n fixes one :: 'a (\\<open>1\\<close>)",
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"class plus =\n fixes plus :: \"'a \\<Righta... | [
"\\<lbrakk> ?H1 x_1; ?H2 (?H3 x_1) (?H4 x_1) = ?H5 x_1; ?H6 < ?H7 (?H8 x_1 (?H9 (?H10 (?H11 x_1) (?H12 (\\<lambda>y_0. ?H13) (?H14 (\\<lambda>y_1. y_1 \\<le> ?H13)))) (?H11 x_1))) (?H11 x_1)\\<rbrakk> \\<Longrightarrow> ?H15 (\\<lambda>y_2. ?H16 < ?H8 x_1 (?H9 (?H10 (?H11 x_1) (?H12 (\\<lambda>y_3. ?H13) (?H14 (\\<... | 275 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_diff_eq' | lemma clmm_quote_gross_diff_eq':
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P) "
and "j = lower_tick P sqp"
and "j = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
shows "quote_gross P sqp' - quote_gross P sqp = L j * (sqp' - sqp)" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; j = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'\<rbrakk> \<Longrightarrow> quote_gross P sqp' - quote_gross P sqp = L j * (sqp' - sqp) | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_3 = H5 x_1 x_5; H6 < x_4; x_4 \<le> x_5\<rbrakk> \<Longrightarrow> H7 (H8 x_1 x_5) (H8 x_1 x_4) = H9 (x_2 x_3) (H7 x_5 x_4) | [
"Groups.times_class.times",
"Grid_Information.quote_gross",
"Groups.minus_class.minus",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a \\<Rightarrow> 'a \\<Rightarrow> 'a",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (... | [
"class times =\n fixes times :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>*\\<close> 70)",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class minus =\n fixes minus :: \"'a \\<Rightarrow> 'a \\<Rightarrow> 'a\" (infixl \\<open>-\\<close> ... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H2 x_4 x_5; ?H3 x_1 = ?H3 x_4; ?H4 x_1 = ?H4 x_4; ?H5 x_1 = ?H5 x_4; ?H6 x_1 = ?H6 x_4; ?H7 \\<le> x_6; ?H7 \\<le> x_3 x_6; ?H8 x_3 x_6 \\<le> ?H9 x_1 x_6; ?H8 (?H10 (?H9 x_1 x_6) (?H5 x_1)) (?H9 x_4 x_6) \\<le> ?H9 x_4 x_6\\<rbrakk> \\<Longrightarrow> ?H8 (?H10 (?H9 x_1 x_6) (?H... | 194 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_eq_lower_only_if | lemma clmm_quote_gross_eq_lower_only_if:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
and "quote_gross P sqp' = quote_gross P sqp"
shows "L j = 0" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k; quote_gross P sqp' = quote_gross P sqp\<rbrakk> \<Longrightarrow> L j = 0 | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5; H7 x_1 x_6 = H7 x_1 x_4\<rbrakk> \<Longrightarrow> x_2 x_3 = H6 | [
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> int",
"(int \\<Rightarrow... | [
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P prc)\"",
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H2 x_4 x_5; ?H3 x_1 = ?H3 x_4; ?H4 x_1 = ?H4 x_4; ?H5 x_1 = ?H5 x_4; ?H6 x_1 = ?H6 x_4; ?H7 \\<le> x_3; ?H7 \\<le> x_5\\<rbrakk> \\<Longrightarrow> ?H8 x_1 x_3 = ?H8 x_4 x_5"
] | 92 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_eq_lower_only_if' | lemma clmm_quote_gross_eq_lower_only_if':
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P) "
and "j = lower_tick P sqp"
and "j = lower_tick P sqp'"
and "0 < sqp"
and "sqp < sqp'"
and "quote_gross P sqp' = quote_gross P sqp"
shows "L j = 0" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; j = lower_tick P sqp'; 0 < sqp; sqp < sqp'; quote_gross P sqp' = quote_gross P sqp\<rbrakk> \<Longrightarrow> L j = 0 | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_3 = H5 x_1 x_5; H6 < x_4; x_4 < x_5; H7 x_1 x_5 = H7 x_1 x_4\<rbrakk> \<Longrightarrow> x_2 x_3 = H6 | [
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> int",
"(int \\<Rightarrow... | [
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P prc)\"",
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H2 x_4 x_5; ?H3 x_1 = ?H3 x_4; ?H4 x_1 = ?H4 x_4; ?H5 x_1 = ?H5 x_4; ?H6 x_1 = ?H6 x_4; ?H7 \\<le> x_3; ?H7 \\<le> x_5\\<rbrakk> \\<Longrightarrow> ?H8 x_1 x_3 = ?H8 x_4 x_5"
] | 86 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_eq_sum_emp | lemma clmm_quote_gross_eq_sum_emp:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
and "quote_gross P sqp' = quote_gross P sqp"
shows "{i. L i \<noteq> 0 \<and> j <i \<and> i < k} = {}" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k; quote_gross P sqp' = quote_gross P sqp\<rbrakk> \<Longrightarrow> {i. L i \<noteq> 0 \<and> j < i \<and> i < k} = {} | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5; H7 x_1 x_6 = H7 x_1 x_4\<rbrakk> \<Longrightarrow> H8 (\<lambda>y_0. x_2 y_0 \<noteq> H6 \<and> x_3 < y_0 \<and> y_0 < x_5) = H9 | [
"Set.empty",
"Set.Collect",
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"'a set",
"('a \\<Rightarrow> bool) \\<Rightarrow> 'a set",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)... | [
"abbreviation empty :: \"'a set\" (\\<open>{}\\<close>)\n where \"{} \\<equiv> bot\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P ... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H3 x_1; ?H4 x_1 = ?H5 x_1; ?H6 x_1 = ?H7\\<rbrakk> \\<Longrightarrow> ?H8 x_1 x_4 \\<in> ?H9 (\\<lambda>y_0. ?H7 \\<le> x_2 y_0 \\<and> x_2 y_0 \\<le> x_3 y_0) \\<and> ?H8 x_1 x_4 \\<noteq> ?H7 \\<and> ?H8 x_1 x_4 < x_4 \\<and> x_4 < ?H7 \\<and> ?H8 x_1 x_4 = ?H8 x_1 x_4 \\<and> ... | 230 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_eq_sum_only_if | lemma clmm_quote_gross_eq_sum_only_if:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
and "quote_gross P sqp' = quote_gross P sqp"
and "j < i"
and "i < k"
shows "L i = 0" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k; quote_gross P sqp' = quote_gross P sqp; j < i; i < k\<rbrakk> \<Longrightarrow> L i = 0 | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5; H7 x_1 x_6 = H7 x_1 x_4; x_3 < x_7; x_7 < x_5\<rbrakk> \<Longrightarrow> x_2 x_7 = H6 | [
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> int",
"(int \\<Rightarrow... | [
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (rng_blw P prc)\"",
"definition fee::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H2 x_4 x_5; ?H3 x_1 = ?H3 x_4; ?H4 x_1 = ?H4 x_4; ?H5 x_1 = ?H5 x_4; ?H6 x_1 = ?H6 x_4; ?H7 \\<le> x_3; ?H7 \\<le> x_5\\<rbrakk> \\<Longrightarrow> ?H8 x_1 x_3 = ?H8 x_4 x_5"
] | 100 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_eq_upper_only_if | lemma clmm_quote_gross_eq_upper_only_if:
assumes "clmm_dsc P"
and "L = gross_fct (lq P) (fee P)"
and "j = lower_tick P sqp"
and "k = lower_tick P sqp'"
and "0 < sqp"
and "sqp \<le> sqp'"
and "j < k"
and "quote_gross P sqp' = quote_gross P sqp"
shows "L k = 0 \<or> grd P k = sqp'" | \<lbrakk>clmm_dsc P; L = gross_fct (lq P) (fee P); j = lower_tick P sqp; k = lower_tick P sqp'; 0 < sqp; sqp \<le> sqp'; j < k; quote_gross P sqp' = quote_gross P sqp\<rbrakk> \<Longrightarrow> L k = 0 \<or> grd P k = sqp' | \<lbrakk>H1 x_1; x_2 = H2 (H3 x_1) (H4 x_1); x_3 = H5 x_1 x_4; x_5 = H5 x_1 x_6; H6 < x_4; x_4 \<le> x_6; x_3 < x_5; H7 x_1 x_6 = H7 x_1 x_4\<rbrakk> \<Longrightarrow> x_2 x_5 = H6 \<or> H8 x_1 x_5 = x_6 | [
"Grid_Information.grd",
"Grid_Information.quote_gross",
"Groups.zero_class.zero",
"CLMM_Description.lower_tick",
"Grid_Information.fee",
"Grid_Information.lq",
"CLMM_Misc.gross_fct",
"CLMM_Description.clmm_dsc"
] | [
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> int \\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a",
"(int \\<Rightarrow... | [
"definition grd::\"grid_info \\<Rightarrow> (int\\<Rightarrow> real)\" where\n\"grd P = fst P\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition lower_tick where\n\"lower_tick P prc = Sup (... | [
"\\<lbrakk> ?H1 x_1; ?H2 x_2 x_3 = ?H2 x_4 x_5; ?H3 x_1 = ?H3 x_4; ?H4 x_1 = ?H4 x_4; ?H5 x_1 = ?H5 x_4; ?H6 x_1 = ?H6 x_4; ?H7 < x_3; ?H7 < x_5\\<rbrakk> \\<Longrightarrow> ?H8 x_1 = ?H8 x_4 \\<and> ?H9 x_1 = ?H9 x_4"
] | 94 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
both | local | template | full | deepseek-coder-1.3b-base | afp_2026_entries | template_afp_2026_entries | template_full | yalhessi/lemexp-task1-v3-template_full-deepseek-coder-1.3b-base-8lr-12epochs-normal-eos | Concentrated_Liquidity_Market_Making_Operations/CLMM_Description | CLMM_Description.clmm_quote_gross_grd_min | lemma clmm_quote_gross_grd_min:
assumes "clmm_dsc P"
and "nz_support (lq P) \<noteq> {}"
shows "quote_gross P (grd_min P) = 0" | \<lbrakk>clmm_dsc P; nz_support (lq P) \<noteq> {}\<rbrakk> \<Longrightarrow> quote_gross P (grd_min P) = 0 | \<lbrakk>H1 x_1; H2 (H3 x_1) \<noteq> H4\<rbrakk> \<Longrightarrow> H5 x_1 (H6 x_1) = H7 | [
"Groups.zero_class.zero",
"Grid_Information.grd_min",
"Grid_Information.quote_gross",
"Set.empty",
"Grid_Information.lq",
"CLMM_Misc.nz_support",
"CLMM_Description.clmm_dsc"
] | [
"'a",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real",
"(int \\<Rightarrow> real) \\<times>\n(int \\<Rightarrow> real) \\<times> (int \\<Rightarrow> real)\n\\<Rightarrow> real \\<Rightarrow> real",
"'a set",
"(int \\<Rightarrow> real)... | [
"class zero =\n fixes zero :: 'a (\\<open>0\\<close>)",
"definition grd_min where\n \"grd_min P = idx_min_img (grd P) (lq P)\"",
"definition quote_gross where\n\"quote_gross P = gen_quote (grd P) (gross_fct (lq P) (fee P))\"",
"abbreviation empty :: \"'a set\" (\\<open>{}\\<close>)\n where \"{} \\<equiv> ... | [
"\\<lbrakk> ?H1 x_1; ?H2 (?H3 x_1) \\<noteq> ?H4\\<rbrakk> \\<Longrightarrow> ?H5 x_1 (?H6 x_1) = ?H7 x_1 \\<and> ?H5 x_1 (?H3 x_1) = ?H8"
] | 43 | false | [
false
] | 0 | false | false | 0 | false | 0 | false |
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