hcju/isabelleps huggingface dataset:
sub_inter_l2: fixes T1 :: "funty"   and T2 :: "funty" shows "T1 \<sqinter> T2 <:: T2"
norm_ACI_if_nf_ACI: fixes \<phi> :: "('a, 'b) aformula" assumes "nf_ACI \<phi>" shows "\<langle>\<phi>\<rangle> = \<phi>"
strict_prefix_def: fixes xs :: "'c list"   and ys :: "'c list" shows "strict_prefix xs ys = (prefix xs ys \<and> xs \<noteq> ys)"
hypsubst: fixes A :: "'a set"   and B :: "'a set"   and x :: "'a" assumes "A = B"   and "x \<in> B" obtains "x \<in> A"
amin_amult_pos: fixes z :: "int"   and x :: "ant"   and y :: "ant" assumes "0 < z" shows "amin (ant z * x) (ant z * y) = ant z * amin x y"
map_restrict_insert_none_simp: fixes m :: "'b \<Rightarrow> 'a option"   and x :: "'b"   and s :: "'b set" assumes "m x = None" shows "m |` (- insert x s) = m |` (- s)"
assms_2: shows "hn_refine \<Gamma> c \<Gamma>' R a"
sub: shows "P \<turnstile> C' \<prec>\<^sup>1 D"
CONSTRAINT_def: fixes f :: "'d"   and R :: "('e \<times> 'd) set" shows "Autoref_Fix_Rel.CONSTRAINT f R \<equiv> True"
inject_4: fixes x41 :: "nat"   and x42 :: "exp list"   and y41 :: "nat"   and y42 :: "exp list" shows "(New x41 x42 = New y41 y42) = (x41 = y41 \<and> x42 = y42)"
not_ordLess_ordIso: fixes r :: "('c \<times> 'c) set"   and r' :: "('d \<times> 'd) set" assumes "r <o r'" shows "(r, r') \<notin> ordIso"
bbind_strict2: fixes x :: "'b\<^sub>\<bottom>" shows "x >>= \<bottom> = \<bottom>"
EmptyMap_Union_ran_override2: fixes S :: "'d set"   and G1 :: "'d \<Rightarrow> ('d, 'e, 'f) seqauto set option"   and G2 :: "'d \<Rightarrow> ('d, 'e, 'f) seqauto set option" assumes "S \<noteq> {}"   and "S \<inter> dom G1 = {}"   and "dom G1 \<inter> dom G2 = {}" shows "\<Union> (ran (G1 ++ EmptyMap S ++ G2)) = \<Union> (ran G1 \<union> ran G2)"
hext_objD: fixes h :: "heap"   and h' :: "heap"   and a :: "nat"   and C :: "char list"   and fs :: "Objects.fields" assumes "h \<unlhd> h'"   and "h a = \<lfloor>(C, fs)\<rfloor>" shows "\<exists>fs'. h' a = \<lfloor>(C, fs')\<rfloor>"
akra_bazzi_lower_axioms: shows "akra_bazzi_lower x\<^sub>0 x\<^sub>1 k as bs ts f integrable integral g g'"
slength_sfoldl_aux: fixes z :: "Integer"   and xs :: "[:'r:]" shows "sfoldl\<cdot>(\<Lambda> i uu_. i + 1)\<cdot>z\<cdot>xs = z + slength\<cdot>xs"
right_total_rel_gpv': fixes A :: "'g \<Rightarrow> 'h \<Rightarrow> bool"   and C :: "'i \<Rightarrow> 'j \<Rightarrow> bool"   and R :: "'k \<Rightarrow> 'l \<Rightarrow> bool" assumes "right_total A"   and "right_total C"   and "right_unique R"   and "left_total R" shows "right_total (rel_gpv'' A C R)"
elims: fixes x :: "'b hp list"   and y :: "nat" assumes "size_hps x = y" obtains xa :: "'b" and hsl :: "'b hp list" and hsr :: "'b hp list" where "x = Hp xa hsl # hsr" and "y = size_hps hsl + size_hps hsr + 1"   | "x = []" and "y = 0"
that: fixes m :: "nat"   and n :: "nat" assumes "\<phi> m = \<phi> (the (g m n))"   and "\<phi> n = \<phi> (the (h m n))" shows "thesis"
intro: fixes hom :: "'a \<Rightarrow> 'b" assumes "\<And>x y. hom (x + y) = hom x + hom y" shows "plus_hom hom"
Group_def: fixes G :: "('e, 'f) Group_scheme" shows "Group G \<equiv> ((\<cdot>\<^bsub>G\<^esub>) \<in> carrier G \<rightarrow> carrier G \<rightarrow> carrier G \<and> (\<forall>a b c. a \<in> carrier G \<longrightarrow> b \<in> carrier G \<longrightarrow> c \<in> carrier G \<longrightarrow> a \<cdot>\<^bsub>G\<^esub> b \<cdot>\<^bsub>G\<^esub> c = a \<cdot>\<^bsub>G\<^esub> (b \<cdot>\<^bsub>G\<^esub> c)) \<and> iop G \<in> carrier G \<rightarrow> carrier G) \<and> (\<forall>a. a \<in> carrier G \<longrightarrow> \<rho>\<^bsub>G\<^esub> a \<cdot>\<^bsub>G\<^esub> a = \<one>\<^bsub>G\<^esub>) \<and> \<one>\<^bsub>G\<^esub> \<in> carrier G \<and> (\<forall>a. a \<in> carrier G \<longrightarrow> \<one>\<^bsub>G\<^esub> \<cdot>\<^bsub>G\<^esub> a = a)"
closed_Collect_disj: fixes P :: "'a \<Rightarrow> bool"   and Q :: "'a \<Rightarrow> bool" assumes "closed {x. P x}"   and "closed {x. Q x}" shows "closed {x. P x \<or> Q x}"
c_tr_hd_tl: fixes xs :: "'e list"   and step :: "'g \<Rightarrow> 'e \<Rightarrow> 'g"   and out :: "'g \<Rightarrow> 'e \<Rightarrow> 'f"   and s :: "'g" assumes "xs \<noteq> []" shows "c_tr step out s xs = (hd xs, out s (hd xs)) # c_tr step out (step s (hd xs)) (tl xs)"
Dirichlet_L_nonprincipal_mangoldt_bound_aux_strong: fixes x :: "real" assumes "0 < x" shows "cmod (L * sum_upto (\<lambda>k. \<chi> k * mangoldt k / of_nat k) x - sum_upto (\<lambda>k. \<chi> k * complex_of_real (ln (real k)) / of_nat k) x) \<le> 9 / 2 * real (totient n)"
Quotient3_ltl_prop_equiv_quotient: shows "Quotient3 (\<equiv>\<^sub>P) Abs Rep"
simps_9: fixes sent' :: "('g \<Rightarrow> 'g set) \<Rightarrow> 'g \<Rightarrow> 'g set"   and round :: "'g \<Rightarrow> nat"   and state :: "'g \<Rightarrow> 'f"   and sent :: "'g \<Rightarrow> 'g set"   and rcvd :: "'g \<Rightarrow> 'g \<Rightarrow> 'h option"   and network :: "('g \<times> nat \<times> 'g \<times> 'h) set"   and more :: "'i" shows "sent_update sent' \<lparr>round = round, state = state, sent = sent, rcvd = rcvd, network = network, \<dots> = more\<rparr> = \<lparr>round = round, state = state, sent = sent' sent, rcvd = rcvd, network = network, \<dots> = more\<rparr>"
simps_10: fixes prec :: "nat"   and ord :: "nat"   and I :: "float interval list"   and a :: "float interval list"   and f :: "floatarith"   and env :: "taylor_model list" shows "approx_tm prec ord I a (Exp f) env = compute_tm_by_comp prec ord I a (Exp (Var 0)) (approx_tm prec ord I a f env) (\<lambda>x. True)"
empty_list_nin_state_set: fixes h :: "('a, 'b) fmap"   and slist :: "('a, 'b) fmap list"   and s :: "('a, 'b) fmap"   and as :: "(('a, 'b) fmap \<times> ('a, 'b) fmap) list" assumes "h # slist \<in> state_set (state_list s as)" shows "h = s"
inf_sup_aci_2: fixes inf :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type"   and less_eq :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> bool"   and less :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> bool"   and sup :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type"   and x :: "'b::type"   and y :: "'b::type"   and z :: "'b::type" assumes "class.lattice (inf::'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type) (less_eq::'b::type \<Rightarrow> 'b::type \<Rightarrow> bool) (less::'b::type \<Rightarrow> 'b::type \<Rightarrow> bool) (sup::'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type)" shows "(inf::'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type) (inf (x::'b::type) (y::'b::type)) (z::'b::type) = inf x (inf y z)"
assms_5: shows "(r, Store e2 mo r) \<in> set (node_deliver_messages xs)"
trnl\<^sub>\<eta>_def: fixes v :: "'a"   and \<mu> :: "'a" shows "A'.trnl\<^sub>\<eta> v \<mu> \<equiv> (g' \<star> \<mu>) \<cdot> \<a>[g', f, v] \<cdot> (\<eta>' \<star> v) \<cdot> \<l>\<^sup>-\<^sup>1[v]"
map_disc_iff: fixes f :: "'d \<Rightarrow> 'c"   and a :: "'d option" shows "(map_option f a = None) = (a = None)"
inject_1: fixes x21 :: "'a tree23"   and x22 :: "int \<times> 'a"   and x23 :: "'a tree23"   and y21 :: "'a tree23"   and y22 :: "int \<times> 'a"   and y23 :: "'a tree23" shows "(Branch2 x21 x22 x23 = Branch2 y21 y22 y23) = (x21 = y21 \<and> x22 = y22 \<and> x23 = y23)"
assms_4: shows "\<forall>x\<in>P. finite (cl_ecl x)"
inject_3: fixes x3 :: "('b, 'c) fm"   and y3 :: "('b, 'c) fm" shows "((\<^bold>\<not> x3) = (\<^bold>\<not> y3)) = (x3 = y3)"
Dhyp: shows "D (\<lambda>t. \<phi> t s) \<mapsto> (\<lambda>\<tau>. \<tau> *\<^sub>R f (\<phi> t s)) at t within B"
num_reachable_norefl_def: fixes G :: "'b graph"   and v :: "'b" shows "FiniteGraph.num_reachable_norefl G v = card (FiniteGraph.succ_tran G v - {v})"
nact_active: fixes id :: "'nid"   and t :: "nat \<Rightarrow> cnf"   and n :: "nat"   and n'' :: "nat" assumes "\<parallel>id\<parallel>\<^bsub>t n\<^esub>"   and "n \<le> n''"   and "\<not> (\<exists>n'\<ge>n. latestAct_cond id t n'' n')" shows "n = n''"
binrelchain_append_reduce2: fixes P :: "'b \<Rightarrow> 'b \<Rightarrow> bool"   and xs :: "'b list"   and ys :: "'b list" assumes "binrelchain P (xs @ ys)" shows "binrelchain P ys"
a1: shows "low_equal s1 s2 \<and> (fst instr = load_store_type LDSB \<or> fst instr = load_store_type LDUB \<or> fst instr = load_store_type LDUBA \<or> fst instr = load_store_type LDUH \<or> fst instr = load_store_type LD \<or> fst instr = load_store_type LDA \<or> fst instr = load_store_type LDD) \<and> get_S (cpu_reg_val PSR s1) = 0 \<and> get_S (cpu_reg_val PSR s2) = 0 \<and> t1 = snd (fst (load_instr instr s1)) \<and> t2 = snd (fst (load_instr instr s2))"
sum_list_vdiff_distr: fixes v :: "nat list"   and u :: "nat list" assumes "v \<le>\<^sub>v u" shows "sum_list (u -\<^sub>v v) = sum_list u - sum_list v"
rpr_choiceFn: fixes A :: "'c set"   and r :: "('c \<times> 'c) set" assumes "finite A"   and "rpr A r" shows "choiceFn A r"
LeftDerivationIntro_def: fixes \<alpha> :: "symbol list"   and i :: "nat"   and r :: "symbol \<times> symbol list"   and ix :: "nat"   and D :: "(nat \<times> symbol \<times> symbol list) list"   and j :: "nat"   and \<gamma> :: "symbol list" shows "LeftDerivationIntro \<alpha> i r ix D j \<gamma> = (\<exists>\<beta>. LeftDerives1 \<alpha> i r \<beta> \<and> ix < length (snd r) \<and> snd r ! ix = \<gamma> ! j \<and> LeftDerivationFix \<beta> (i + ix) D j \<gamma>)"
eq2: shows "{A \<in> \<A>. X closure_of A \<inter> V \<noteq> {}} = {A \<in> \<A>. A \<inter> V \<noteq> {}}"
ipurge_rec_ext_def: fixes Pol :: "('d \<times> 'd) set"   and Map :: "'c \<Rightarrow> 'd"   and Dom :: "'d"   and In :: "'c list"   and Out :: "'c list"   and more :: "'e" shows "\<lparr>Pol = Pol, Map = Map, Dom = Dom, In = In, Out = Out, \<dots> = more\<rparr> \<equiv> Record.iso_tuple_cons ipurge_rec_ext_Tuple_Iso (Record.iso_tuple_cons Record.tuple_iso_tuple (Record.iso_tuple_cons Record.tuple_iso_tuple Pol Map) (Record.iso_tuple_cons Record.tuple_iso_tuple Dom (Record.iso_tuple_cons Record.tuple_iso_tuple In Out))) more"
Enabled_disj1: fixes F :: "(nat \<Rightarrow> 'a) \<Rightarrow> bool"   and G :: "(nat \<Rightarrow> 'a) \<Rightarrow> bool" shows "\<turnstile> Enabled F \<longrightarrow> Enabled (F \<or> G)"
exhaust_sel: fixes option :: "'h option" obtains "option = None"   | "option = Some (the option)"
Inf_superset_mono: fixes Inf :: "'b::type set \<Rightarrow> 'b::type"   and Sup :: "'b::type set \<Rightarrow> 'b::type"   and inf :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type"   and less_eq :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> bool"   and less :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> bool"   and sup :: "'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type"   and bot :: "'b::type"   and top :: "'b::type"   and B :: "'b::type set"   and A :: "'b::type set" assumes "class.complete_lattice (Inf::'b::type set \<Rightarrow> 'b::type) (Sup::'b::type set \<Rightarrow> 'b::type) (inf::'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type) (less_eq::'b::type \<Rightarrow> 'b::type \<Rightarrow> bool) (less::'b::type \<Rightarrow> 'b::type \<Rightarrow> bool) (sup::'b::type \<Rightarrow> 'b::type \<Rightarrow> 'b::type) (bot::'b::type) (top::'b::type)"   and "(B::'b::type set) \<subseteq> (A::'b::type set)" shows "(less_eq::'b::type \<Rightarrow> 'b::type \<Rightarrow> bool) ((Inf::'b::type set \<Rightarrow> 'b::type) (A::'b::type set)) (Inf (B::'b::type set))"
proves_eq_symmetric: fixes \<Theta> :: "((String.literal \<Rightarrow> typ option) \<times> (String.literal \<Rightarrow> nat option) \<times> (String.literal \<times> String.literal) set \<times> (String.literal \<Rightarrow> (String.literal \<Rightarrow> String.literal set list option) option)) \<times> Core.term set"   and t :: "Core.term"   and s :: "Core.term"   and \<Gamma> :: "Core.term set" assumes "wf_theory \<Theta>"   and "term_ok \<Theta> t"   and "term_ok \<Theta> s"   and "typ_of s = typ_of t"   and "finite \<Gamma>"   and "\<forall>A\<in>\<Gamma>. term_ok \<Theta> A"   and "\<forall>A\<in>\<Gamma>. typ_of A = Some propT" shows "\<Theta>,\<Gamma> \<turnstile> mk_eq s t \<longmapsto> mk_eq t s"
unambiguous_routing_Cons: fixes r :: "('b, 'c) routing_rule_scheme"   and rtbl :: "('b, 'c) routing_rule_scheme list" assumes "unambiguous_routing (r # rtbl)" shows "unambiguous_routing rtbl"
servTicket_authentic: fixes B :: "agent"   and A :: "agent"   and servK :: "nat"   and Ts :: "nat"   and evs :: "event list" assumes "Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace> \<in> parts (knows Spy evs)"   and "B \<noteq> Tgs"   and "B \<notin> bad"   and "evs \<in> kerbV" shows "\<exists>Ta authK. Says Kas A \<lbrace>Crypt (shrK A) \<lbrace>Key authK, Agent Tgs, Number Ta\<rbrace>, Crypt (shrK Tgs) \<lbrace>Agent A, Agent Tgs, Key authK, Number Ta\<rbrace>\<rbrace> \<in> set evs \<and> Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, Number Ts\<rbrace>, Crypt (shrK B) \<lbrace>Agent A, Agent B, Key servK, Number Ts\<rbrace>\<rbrace> \<in> set evs"
dom_cod: fixes f :: "'c" assumes "J'.arr f" shows "J'.dom (J'.cod f) = J'.cod f"
simps: fixes a1 :: "comb"   and a2 :: "comb" shows "(a1 \<Rrightarrow>\<^sup>1 a2) = ((\<exists>x. a1 = x \<and> a2 = x) \<or> (\<exists>x y. a1 = K \<bullet> x \<bullet> y \<and> a2 = x) \<or> (\<exists>x y z. a1 = S \<bullet> x \<bullet> y \<bullet> z \<and> a2 = x \<bullet> z \<bullet> (y \<bullet> z)) \<or> (\<exists>x y z w. a1 = x \<bullet> z \<and> a2 = y \<bullet> w \<and> x \<Rrightarrow>\<^sup>1 y \<and> z \<Rrightarrow>\<^sup>1 w))"
disjunct_not_in: fixes A :: "'k multiset"   and B :: "'k multiset" shows "(A \<inter># B = {#}) = (\<forall>a. a \<notin># A \<or> a \<notin># B)"
N_below_pp: fixes x :: "'a" shows "N x \<le> - - x"
conj_superexpansion1: fixes Cn :: "'b set \<Rightarrow> 'b set"   and true_PL :: "'b"   and false_PL :: "'b"   and imp_PL :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and not_PL :: "'b \<Rightarrow> 'b"   and conj_PL :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and disj_PL :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and equiv_PL :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and p :: "'b"   and q :: "'b"   and A :: "'b set" assumes "Supraclassical_logic Cn true_PL false_PL imp_PL not_PL conj_PL disj_PL equiv_PL" shows "(conj_PL (not_PL (conj_PL p q)) (not_PL p) \<in> Cn A) = (not_PL p \<in> Cn A)"
split_gallery: fixes C :: "'a set"   and D :: "'a set"   and Cs :: "'a set list" assumes "C \<in> f \<turnstile> folding.\<C>"   and "D \<in> folding.\<C> - f \<turnstile> folding.\<C>"   and "folding.gallery (C # Cs @ [D])" shows "\<exists>As A B Bs. A \<in> f \<turnstile> folding.\<C> \<and> B \<in> folding.\<C> - f \<turnstile> folding.\<C> \<and> C # Cs @ [D] = As @ A # B # Bs"
gamma_is_in_terms_of_i: shows "\<gamma> = (\<lambda>x. f x *\<^sub>R i + g (f x))"
assms_3: shows "r\<^sup>*\<^sup>* x y2"
assms_2: shows "finite {a. \<exists>b. P a b}"
S1_Returndisabled: fixes rmhist :: "state \<Rightarrow> PrIds \<Rightarrow> histState"   and p :: "PrIds" shows "\<turnstile> S1 rmhist p \<longrightarrow> \<not> Enabled (<MemReturn memCh (resbar rmhist) p>_(rtrner memCh!p, resbar rmhist!p))"
vars\<^sub>s\<^sub>t_def: fixes S :: "('d, 'c) strand_step list" shows "vars\<^sub>s\<^sub>t S \<equiv> \<Union> (set (map vars\<^sub>s\<^sub>t\<^sub>p S))"
subst_idemI': fixes \<sigma> :: "'a \<Rightarrow> ('b, 'a) Term.term" assumes "ground (subst_range \<sigma>)" shows "subst_idem \<sigma>"
rsub_1: shows "r ` {x. 0 \<le> x (Suc n)} \<subseteq> {x. 0 \<le> x (Suc n)}"
isomorphic_implies_hpar_3: fixes f :: "'b"   and f' :: "'b" assumes "D.isomorphic f f'" shows "src\<^sub>D f = src\<^sub>D f'"
all_comm: fixes P :: "'d \<Rightarrow> 'e \<Rightarrow> bool" shows "(\<forall>x y. P x y) = (\<forall>y x. P x y)"
syncTlEmpty: fixes a :: "'a event list"   and A :: "'a event set"   and u :: "'a event list" assumes "a setinterleaves (([], u), A)" shows "tl a setinterleaves (([], tl u), A)"
lub_singleton_def: fixes lub :: "'c set \<Rightarrow> 'c" shows "lub_singleton lub = (\<forall>a. lub {a} = a)"
is_orthogonal_closure: fixes S :: "'b set"   and a :: "'b"   and x :: "'b" assumes "\<And>s. s \<in> S \<Longrightarrow> is_orthogonal a s"   and "x \<in> closure S" shows "is_orthogonal a x"
sum_list_eq_nthI: fixes i :: "nat"   and xs :: "'a list" assumes "i < length xs"   and "\<And>j. \<lbrakk>j < length xs; j \<noteq> i\<rbrakk> \<Longrightarrow> xs ! j = (0::'a)" shows "sum_list xs = xs ! i"
get_child_nodes_ok: fixes ptr :: "(_) object_ptr"   and h :: "(_) heap" assumes "ShadowRootClass.known_ptr ptr"   and "ShadowRootClass.type_wf h"   and "ptr |\<in>| object_ptr_kinds h" shows "h \<turnstile> ok Shadow_DOM.get_child_nodes ptr"
simps: fixes cms :: "'Com \<times> (Mode \<Rightarrow> 'Var set)"   and mem :: "'Var \<Rightarrow> 'Val"   and cms' :: "'Com \<times> (Mode \<Rightarrow> 'Var set)"   and mem' :: "'Var \<Rightarrow> 'Val"   and X :: "'Var set"   and g :: "('Var \<Rightarrow> 'Val option) \<Rightarrow> 'Var \<Rightarrow> 'Val option" shows "change_respecting (cms, mem) (cms', mem') X g = ((cms, mem) \<leadsto> (cms', mem') \<and> (\<forall>\<sigma>. dom \<sigma> = X \<longrightarrow> g \<sigma> \<preceq> \<sigma>) \<and> (\<forall>\<sigma> \<sigma>'. dom \<sigma> = X \<and> dom \<sigma>' = X \<longrightarrow> dom (g \<sigma>) = dom (g \<sigma>')) \<and> (\<forall>\<sigma>. dom \<sigma> = X \<longrightarrow> (cms, subst \<sigma> mem) \<leadsto> (cms', subst (g \<sigma>) mem')))"
rel_of_succ_def: fixes s :: "'c \<Rightarrow> 'd set" shows "rel_of_succ s \<equiv> {(a, b). b \<in> s a}"
inject: fixes x2 :: "'c"   and y2 :: "'c" shows "(\<lbrakk>x2\<rbrakk> = \<lbrakk>y2\<rbrakk>) = (x2 = y2)"
cobounded2: fixes a :: "'e"   and b :: "'e" shows "inf a b \<le> b"
rerename_rename_noop: fixes "from" :: "nat"   and V :: "'var set"   and form :: "'form"   and to :: "nat"   and f :: "'var \<Rightarrow> 'var" assumes "freshenLC from ` V \<inter> lconsts form = {}" shows "renameLCs (rerename V from to f) form = renameLCs f form"
simps_15: fixes Vs :: "char list list"   and e\<^sub>1 :: "char list exp"   and C :: "char list"   and V :: "char list"   and e\<^sub>2 :: "char list exp" shows "compE\<^sub>1 Vs (try e\<^sub>1 catch(C V) e\<^sub>2) = try compE\<^sub>1 Vs e\<^sub>1 catch(C length Vs) compE\<^sub>1 (Vs @ [V]) e\<^sub>2"
exact5_def: fixes R :: "('e, 'f) Ring_scheme"   and L0 :: "('g, 'e, 'h) Module_scheme"   and h0 :: "'g \<Rightarrow> 'i"   and L1 :: "('i, 'e, 'h) Module_scheme"   and h1 :: "'i \<Rightarrow> 'j"   and L2 :: "('j, 'e, 'h) Module_scheme"   and h2 :: "'j \<Rightarrow> 'k"   and L3 :: "('k, 'e, 'h) Module_scheme"   and h3 :: "'k \<Rightarrow> 'l"   and L4 :: "('l, 'e, 'h) Module_scheme" shows "exact5 R L0 h0 L1 h1 L2 h2 L3 h3 L4 \<equiv> h0 ` carrier L0 = ker\<^bsub>L1,L2\<^esub> h1 \<and> h1 ` carrier L1 = ker\<^bsub>L2,L3\<^esub> h2 \<and> h2 ` carrier L2 = ker\<^bsub>L3,L4\<^esub> h3"
C1_differentiable_on_ident: fixes S :: "real set" shows "(\<lambda>x. x) C1_differentiable_on S"
rpo_basis_axioms: shows "rpo_basis ground_heads_var (>\<^sub>s) arity_sym arity_var extf"
induct: fixes P :: "floatarith list \<Rightarrow> floatarith list \<Rightarrow> bool"   and a0 :: "floatarith list"   and a1 :: "floatarith list" assumes "\<And>uu_. P [] uu_"   and "\<And>v va. P (v # va) []"   and "\<And>x xs y ys. P xs ys \<Longrightarrow> P (x # xs) (y # ys)" shows "P a0 a1"
dim_subset_UNIV: fixes S :: "('c, 'd) vec set" shows "vec.dim S \<le> finite_dimensional_vector_space.dimension cart_basis"
mat_of_cols_mult_as_finsum: fixes v :: "'a vec"   and lst :: "'a vec list" assumes "v \<in> carrier_vec (length lst)"   and "\<And>i. i < length lst \<Longrightarrow> lst ! i \<in> carrier_vec n" shows "mat_of_cols n lst *\<^sub>v v = lincomb (\<lambda>l. \<Sum>i = 0..<length lst. if l = lst ! i then v $ i else (0::'a)) (set lst)"
sccs_def: shows "c.sccs \<equiv> {H. induced_subgraph H (G \<restriction> {v. u \<rightarrow>\<^sup>* v}) \<and> strongly_connected H \<and> (\<nexists>H'. induced_subgraph H' (G \<restriction> {v. u \<rightarrow>\<^sup>* v}) \<and> strongly_connected H' \<and> verts H \<subset> verts H')}"
left_partI: fixes v :: "'a"   and u :: "'c"   and s :: "'c"   and t :: "'c" assumes "v \<in> bag u"   and "u \<in> T.left_tree s t" shows "v \<in> left_part s t"
prems_4: shows "wellformed_policy3 (ys @ [y])"
encR: fixes S :: "'procS"   and SRel :: "('procS \<times> 'procS) set"   and TRel :: "('procT \<times> 'procT) set" shows "SourceTerm S \<sim>\<lbrakk>\<cdot>\<rbrakk><SRel,TRel> TargetTerm (\<lbrakk>S\<rbrakk>)"
exec_move_BlockNoneI: fixes ci :: "('addr, 'heap) check_instr"   and P :: "'addr J1_prog"   and t :: "'thread_id"   and e :: "'addr expr1"   and h :: "'heap"   and s :: "'addr val list \<times> 'addr val list \<times> nat \<times> 'addr option"   and ta :: "('addr, 'thread_id, 'heap) jvm_thread_action"   and h' :: "'heap"   and s' :: "'addr val list \<times> 'addr val list \<times> nat \<times> 'addr option"   and V :: "nat"   and T :: "ty" assumes "exec_move ci P t e h s ta h' s'" shows "exec_move ci P t {V:T=None; e} h s ta h' s'"
union_ac_3: fixes M :: "'a multiset"   and N :: "'a multiset"   and K :: "'a multiset" shows "M + (N + K) = N + (M + K)"
simps_3: fixes Ks :: "'a list" shows "combine Ks [] = \<zero>"
return_nondet_def: fixes return :: "'i \<Rightarrow> 'h"   and single :: "'g \<Rightarrow> 'i"   and x :: "'g" shows "nondetM_base.return_nondet return single x = NondetT (return (single x))"
axioms_1: fixes S :: "('a \<times> 'a) set"   and NS :: "('a \<times> 'a) set" assumes "order_pair S NS" shows "pre_order_pair S NS"
partition_spec_def: fixes R :: "'c \<Rightarrow> 'c \<Rightarrow> bool"   and h :: "'d \<Rightarrow> 'c"   and xs :: "'d list"   and lo :: "nat"   and hi :: "nat"   and xs' :: "'d list"   and p :: "nat" shows "partition_spec R h xs lo hi xs' p \<equiv> mset xs' = mset xs \<and> isPartition_map R h xs' lo hi p \<and> lo \<le> p \<and> p \<le> hi \<and> (\<forall>i<lo. xs' ! i = xs ! i) \<and> (\<forall>i. hi < i \<and> i < length xs' \<longrightarrow> xs' ! i = xs ! i)"
irreducibleD2: fixes C :: "'s option set"   and a :: "'s option"   and b :: "'s option" assumes "C \<in> UNIV // K2.communicating"   and "a \<in> C"   and "(a, b) \<in> K2.communicating" shows "b \<in> C"
l1_inv1_init: shows "init l1 \<subseteq> l1_inv1"
wp_true: fixes p :: "('b, 'c) urel" shows "p wp true = true"
sf_aux1: fixes x :: "nat"   and y :: "nat"   and z :: "nat" assumes "x + y < z" shows "sf (x + y) + x < sf z"
search_nonempty_neq0: fixes s :: "nat \<Rightarrow> nat option"   and b :: "nat"   and i :: "nat"   and y\<^sub>0 :: "nat" assumes "total_cons s"   and "s b \<down>= i"   and "\<phi> i y\<^sub>0 \<down>"   and "\<nexists>y. \<phi> i y \<down> \<and> e_length b \<le> y" shows "eval (total_cons.r_search s) [b] \<up>"
inc_i: fixes i :: "'a word"   and m :: "'a word" assumes "1 \<le> i"   and "i < m" shows "1 \<le> i + 1 \<and> i + 1 \<le> m"
bounded_quasi_semilattice_set_def: fixes f :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and top :: "'a"   and bot :: "'a"   and normalize :: "'a \<Rightarrow> 'a" shows "bounded_quasi_semilattice_set f top bot normalize \<equiv> bounded_quasi_semilattice f top bot normalize"
abs_pat_fresh: fixes x :: "name"   and p :: "pat"   and t :: "btrm" shows "x \<sharp> (\<lambda>[p]. t) = (x \<in> supp p \<or> x \<sharp> t)"
cop_F_RH: fixes d :: "'d"   and ds :: "'d set"   and x :: "'x"   and fp :: "'x set" assumes "d \<in> ds"   and "x \<in> Field (Pd d)"   and "aboveS (Pd d) x \<subseteq> Rf CH fp" shows "x \<in> cop_F ds fp"
list_of_llist_of: fixes xs :: "'b list" shows "list_of (llist_of xs) = xs"
I: assumes "Arr t" shows "\<guillemotleft>\<lbrace>t\<rbrace> : \<lbrace>Dom t\<rbrace> \<rightarrow> \<lbrace>Cod t\<rbrace>\<guillemotright>"
NewInitDoneRed: fixes sh :: "sheap"   and C :: "char list"   and sfs :: "sfields"   and h :: "heap"   and l :: "sfields"   and P :: "(char list list \<times> char list exp) prog" assumes "sh C = \<lfloor>(sfs, Done)\<rfloor>" shows "P \<turnstile> \<langle>new C,(h, l, sh),False\<rangle> \<rightarrow> \<langle>new C,(h, l, sh),True\<rangle>"
1: shows "eval_dioph ks (map f xs) + eval_dioph ks (map g xs) = eval_dioph ks (map (\<lambda>x. f x + g x) xs)"
FactGroup_order: fixes H :: "'a set" assumes "subgroup H G"   and "finite H" shows "order G = order (G Mod H) * card H"
elims: fixes x :: "'b heap"   and y :: "nat" assumes "size_hp x = y" obtains "x = heap.Empty" and "y = 0"   | xa :: "'b" and hs :: "'b heap list" where "x = Hp xa hs" and "y = size_hps hs + 1"