hcju/isabelleps huggingface dataset:
assms: fixes x :: "'a" shows "P x \<longrightarrow> Q x"
polyn_deg_add3: fixes p :: "'a"   and q :: "'a"   and n :: "nat" assumes "p \<in> carrier R"   and "p \<noteq> \<zero>"   and "q \<in> carrier R"   and "q \<noteq> \<zero>"   and "p \<plusminus> q \<noteq> \<zero>"   and "deg_n R S X p \<le> n"   and "deg_n R S X q \<le> n" shows "deg_n R S X (p \<plusminus> q) \<le> n"
pr_strict: fixes w :: "'a \<times> nat \<Rightarrow> nat"   and w0 :: "nat"   and pr_strict :: "'a \<times> nat \<Rightarrow> 'a \<times> nat \<Rightarrow> bool"   and pr_weak :: "'a \<times> nat \<Rightarrow> 'a \<times> nat \<Rightarrow> bool"   and least :: "'a \<Rightarrow> bool"   and scf :: "'a \<times> nat \<Rightarrow> nat \<Rightarrow> nat"   and fn :: "'a \<times> nat"   and gm :: "'a \<times> nat" assumes "admissible_kbo w w0 pr_strict pr_weak least scf" shows "pr_strict fn gm = (pr_weak fn gm \<and> \<not> pr_weak gm fn)"
pmf_map: fixes f :: "'b \<Rightarrow> 'a"   and p :: "'b pmf"   and x :: "'a" shows "pmf (map_pmf f p) x = measure_pmf.prob p (f -` {x})"
ZObisL_def: fixes cl :: "('test, 'atom, 'choice) cmd list"   and dl :: "('test, 'atom, 'choice) cmd list" shows "ZObisL cl dl \<equiv> length cl = length dl \<and> (\<forall>n<length cl. cl ! n \<approx>01 dl ! n)"
Lcm_least: fixes one :: "'a"   and zero :: "'a"   and times :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and gcd :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and lcm :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and Gcd :: "'a set \<Rightarrow> 'a"   and Lcm :: "'a set \<Rightarrow> 'a"   and divide :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and plus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and minus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"   and unit_factor :: "'a \<Rightarrow> 'a"   and normalize :: "'a \<Rightarrow> 'a"   and A :: "'a set"   and a :: "'a" assumes "class.semiring_Gcd one zero times gcd lcm Gcd Lcm divide plus minus unit_factor normalize"   and "\<And>b. b \<in> A \<Longrightarrow> dvd.dvd times b a" shows "dvd.dvd times (Lcm A) a"
bounds_compare_contradictory_7: fixes c :: "'c"   and b :: "'c option" assumes "c <\<^sub>l\<^sub>b b"   and "c \<ge>\<^sub>l\<^sub>b b" shows "False"
inter_2: shows "Span K (u # Us) \<inter> Span K Vs = {\<zero>}"
path_contains_classes: fixes P :: "(char list \<times> base list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> char list list \<times> expr) list) list"   and C :: "char list"   and Cs :: "char list list"   and wf_md :: "(char list \<times> base list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> char list list \<times> expr) list) list \<Rightarrow> char list \<Rightarrow> char list \<times> ty list \<times> ty \<times> char list list \<times> expr \<Rightarrow> bool" assumes "Subobjs P C Cs"   and "wf_prog wf_md P" shows "\<forall>C'\<in>set Cs. is_class P C'"
inf_ordering_img: fixes X :: "'a set"   and f :: "nat \<Rightarrow> 'a"   and ord :: "'a \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" assumes "infinite X"   and "TernaryOrdering.ordering f ord X" shows "f ` {0..} = X"
assms_2: shows "N \<subseteq> Pow \<Omega>"
bangInduct': fixes \<Psi> :: "'b"   and P :: "('a, 'b, 'c) psi"   and \<alpha> :: "'a action"   and P' :: "('a, 'b, 'c) psi"   and Prop :: "'d \<Rightarrow> 'b \<Rightarrow> ('a, 'b, 'c) psi \<Rightarrow> 'a action \<Rightarrow> ('a, 'b, 'c) psi \<Rightarrow> bool"   and C :: "'d" assumes "\<Psi> \<rhd> !P \<longmapsto> \<alpha> \<prec> P'"   and "bn \<alpha> \<sharp>* subject \<alpha>"   and "\<And>\<alpha> P' p C. \<lbrakk>bn \<alpha> \<sharp>* \<Psi>; bn \<alpha> \<sharp>* P; bn \<alpha> \<sharp>* subject \<alpha>; bn \<alpha> \<sharp>* C; set p \<subseteq> set (bn \<alpha>) \<times> set (bn (p \<bullet> \<alpha>)); distinctPerm p; bn (p \<bullet> \<alpha>) \<sharp>* \<alpha>; bn (p \<bullet> \<alpha>) \<sharp>* P'; Prop C \<Psi> (P \<parallel> !P) \<alpha> P'\<rbrakk> \<Longrightarrow> Prop C \<Psi> (P \<parallel> !P) (p \<bullet> \<alpha>) (p \<bullet> P')"   and "\<And>\<alpha> P' C. \<lbrakk>\<Psi> \<rhd> P \<longmapsto> \<alpha> \<prec> P'; bn \<alpha> \<sharp>* \<Psi>; bn \<alpha> \<sharp>* P; bn \<alpha> \<sharp>* subject \<alpha>; bn \<alpha> \<sharp>* C; distinct (bn \<alpha>)\<rbrakk> \<Longrightarrow> Prop C \<Psi> (P \<parallel> !P) \<alpha> (P' \<parallel> !P)"   and "\<And>\<alpha> P' C. \<lbrakk>\<Psi> \<rhd> !P \<longmapsto> \<alpha> \<prec> P'; \<And>C. Prop C \<Psi> (!P) \<alpha> P'; bn \<alpha> \<sharp>* \<Psi>; bn \<alpha> \<sharp>* P; bn \<alpha> \<sharp>* subject \<alpha>; bn \<alpha> \<sharp>* C; distinct (bn \<alpha>)\<rbrakk> \<Longrightarrow> Prop C \<Psi> (P \<parallel> !P) \<alpha> (P \<parallel> P')"   and "\<And>M N P' K xvec P'' C. \<lbrakk>\<Psi> \<rhd> P \<longmapsto> M\<lparr>N\<rparr> \<prec> P'; \<Psi> \<rhd> !P \<longmapsto> K\<lparr>\<nu>*xvec\<rparr>\<langle>N\<rangle> \<prec> P''; \<And>C. Prop C \<Psi> (!P) (K\<lparr>\<nu>*xvec\<rparr>\<langle>N\<rangle>) P''; \<Psi> \<turnstile> M \<leftrightarrow> K; xvec \<sharp>* \<Psi>; xvec \<sharp>* P; xvec \<sharp>* M; xvec \<sharp>* K; xvec \<sharp>* C; distinct xvec\<rbrakk> \<Longrightarrow> Prop C \<Psi> (P \<parallel> !P) (\<tau>) (\<lparr>\<nu>*xvec\<rparr>P' \<parallel> P'')"   and "\<And>M xvec N P' K P'' C. \<lbrakk>\<Psi> \<rhd> P \<longmapsto> M\<lparr>\<nu>*xvec\<rparr>\<langle>N\<rangle> \<prec> P'; \<Psi> \<rhd> !P \<longmapsto> K\<lparr>N\<rparr> \<prec> P''; \<And>C. Prop C \<Psi> (!P) (K\<lparr>N\<rparr>) P''; \<Psi> \<turnstile> M \<leftrightarrow> K; xvec \<sharp>* \<Psi>; xvec \<sharp>* P; xvec \<sharp>* M; xvec \<sharp>* K; xvec \<sharp>* C; distinct xvec\<rbrakk> \<Longrightarrow> Prop C \<Psi> (P \<parallel> !P) (\<tau>) (\<lparr>\<nu>*xvec\<rparr>P' \<parallel> P'')"   and "\<And>\<alpha> P' C. \<lbrakk>\<Psi> \<rhd> P \<parallel> !P \<longmapsto> \<alpha> \<prec> P'; guarded P; \<And>C. Prop C \<Psi> (P \<parallel> !P) \<alpha> P'; guarded P; distinct (bn \<alpha>)\<rbrakk> \<Longrightarrow> Prop C \<Psi> (!P) \<alpha> P'" shows "Prop C \<Psi> (!P) \<alpha> P'"
Subobj_last_isClass: fixes wf_md :: "(char list \<times> base list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> char list list \<times> expr) list) list \<Rightarrow> char list \<Rightarrow> char list \<times> ty list \<times> ty \<times> char list list \<times> expr \<Rightarrow> bool"   and P :: "(char list \<times> base list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> char list list \<times> expr) list) list"   and C :: "char list"   and Cs :: "char list list" assumes "wf_prog wf_md P"   and "Subobjs P C Cs" shows "is_class P (last Cs)"
castmsg_simps_4: fixes P :: "'d \<Rightarrow> bool"   and i1 :: "nat"   and i2 :: "nat" shows "castmsg P (connect(i1, i2)) = True"
sel_app_extra_rules_2: fixes x :: "'b" shows "sscase\<cdot>ID\<cdot>\<bottom>\<cdot>(sinl\<cdot>x) = x"
lv_ivl_def: fixes xrs :: "'c list"   and yrs :: "'c list" shows "lv_ivl xrs yrs = {zrs. list_all2 (\<le>) xrs zrs \<and> list_all2 (\<le>) zrs yrs}"
aligned_less_plus_1: fixes x :: "'b word"   and n :: "nat" assumes "is_aligned x n"   and "0 < n" shows "x < x + 1"
insert_seq_start_none: fixes ops :: "('a \<times> 'a option) list"   and xs :: "('a \<times> 'a option) list" assumes "insert_ops ops"   and "insert_seq None xs"   and "insert_ops xs"   and "set xs \<subseteq> set ops" shows "\<forall>i\<in>set (map fst xs). i \<in> set (interp_ins ops)"
complex_eq_cvec_reflp: shows "reflp (\<approx>\<^sub>v)"
my_U_is_defined_1: fixes outcomes :: "'a set"   and \<R> :: "('a pmf \<times> 'a pmf) set"   and p :: "'a pmf" assumes "rational_preference (\<P> outcomes) \<R>"   and "independent_vnm (\<P> outcomes) \<R>"   and "finite outcomes"   and "outcomes \<noteq> {}"   and "continuous_vnm (\<P> outcomes) \<R>"   and "p \<in> \<P> outcomes" shows "my_U outcomes \<R> p \<in> {0..1}"
fds_primepow_subseries_euler_product_cm: fixes f :: "'a fds"   and p :: "nat"   and s :: "'a" assumes "completely_multiplicative_function (fds_nth f)"   and "prime p"   and "abs_conv_abscissa f < ereal (s \<bullet> (1::'a))" shows "eval_fds (fds_primepow_subseries p f) s = (1::'a) / ((1::'a) - fds_nth f p / nat_power p s)"
finiteV: fixes G :: "'a graph" assumes "wf_graph G" shows "finite (nodes G)"
ndet_symm: fixes P :: "'b \<times> 'b \<Rightarrow> bool"   and Q :: "'b \<times> 'b \<Rightarrow> bool" shows "(P \<or> Q) = (Q \<or> P)"
flip_altsublist_adjacent_lists_ball: fixes S :: "'b set" assumes "PreCoxeterSystem S" shows "\<forall>ss\<in>lists S. \<forall>ts. PreCoxeterSystem.flip_altsublist_adjacent ss ts \<longrightarrow> ts \<in> lists S"
DisjointPaths_supergraph: fixes v :: "'a"   and paths :: "'a list set" assumes "DisjointPaths (remove_vertex v) v0 v1 paths" shows "DisjointPaths G v0 v1 paths"
terminalI: fixes x :: "'b"   and subs :: "'b \<Rightarrow> 'b set"   and Gamma :: "'b" assumes "x \<in> subs Gamma" shows "\<not> terminal subs Gamma"
\<epsilon>_def: shows "\<epsilon> \<equiv> transformation_by_components.map (\<cdot>\<^sub>A) (\<cdot>\<^sub>A) FG.map \<epsilon>o"
snth_in: fixes s :: "'b stream"   and X :: "'b set"   and n :: "nat" assumes "s \<in> streams X" shows "s !! n \<in> X"
comp_cod_arr: fixes f :: "('a S.E.term, 'a) S.arr"   and b :: "('a S.E.term, 'a) S.arr" assumes "S.arr f"   and "S.cod f = b" shows "b \<cdot>\<^sub>S f = f"
restrict_Ostrowski_elem: fixes x :: "'a"   and n :: "nat"   and vv :: "nat \<Rightarrow> 'a \<Rightarrow> ant" assumes "x \<in> carrier K"   and "Ostrowski_elem K (Suc (Suc n)) vv x" shows "Ostrowski_elem K (Suc n) vv x"
relpowp_Suc_E: fixes n :: "nat"   and P :: "'a \<Rightarrow> 'a \<Rightarrow> bool"   and x :: "'a"   and z :: "'a" assumes "(P ^^ Suc n) x z" obtains y :: "'a" where "(P ^^ n) x y" and "P y z"
rep_eq: fixes x :: "mini_alg" shows "ma_coeff x = fst (snd (Rep_mini_alg x))"
wf_rels: fixes pointsTo :: "'d \<Rightarrow> ('e, 'f, 'd) ctree" assumes "wf {(l, l'). pointsTo l' = Link l}" shows "wf (rels pointsTo)"
smc_Comp_vdomain_is_composable_arrs: shows "\<D>\<^sub>\<circ> (\<BB>\<lparr>Comp\<rparr>) = composable_arrs \<BB>"
assms: shows "- 1 / 2 \<le> x \<and> x \<le> 1 / 2"
derivable_A: fixes x :: "'a" assumes "derivable x" shows "x \<in> A"
valid_regions_I_cong: fixes I :: "'a \<Rightarrow> intv"   and J :: "'a \<Rightarrow> 'a \<Rightarrow> intv'"   and r :: "('a \<times> 'a) set"   and I' :: "'a \<Rightarrow> intv"   and J' :: "'a \<Rightarrow> 'a \<Rightarrow> intv'" assumes "valid_region X k I J r"   and "\<forall>x\<in>X. I x = I' x"   and "\<forall>x\<in>X. \<forall>y\<in>X. isGreater (I x) \<or> isGreater (I y) \<longrightarrow> J x y = J' x y" shows "region X I J r = region X I' J' r \<and> valid_region X k I' J' r"
list_updates_nth: fixes xs :: "nat list"   and ys :: "'a list"   and vs :: "'a list"   and i :: "nat" assumes "length xs = length ys"   and "distinct xs" shows "list_updates xs ys vs ! i = (if i < length vs \<and> i \<in> set xs then ys ! index xs i else vs ! i)"
contra_subsetD: fixes A :: "'h set"   and B :: "'h set"   and c :: "'h" assumes "A \<subseteq> B"   and "c \<notin> B" shows "c \<notin> A"
Pd_refl: fixes x :: "'a"   and d :: "'b" assumes "x \<in> Field (BPd d)" shows "(x, x) \<in> BPd d"
distinct_11: fixes x3 :: "'b formula" shows "\<bottom> \<noteq> \<^bold>\<not> (x3::'b formula)"
a43: fixes n :: "nat"   and m :: "nat" assumes "0 < n" shows "a ((4 * real m + 3) / 2 ^ Suc n) = rightcut (a ((2 * real m + 1) / 2 ^ n)) (b ((2 * real m + 1) / 2 ^ n)) (c ((2 * real m + 1) / 2 ^ n))"
ring_distribs_3: fixes a :: "'c"   and b :: "'c"   and c :: "'c" shows "(a - b) * c = a * c - b * c"
source_select: fixes a :: "'d"   and b :: "(('d, 'e) expr \<times> ('f data \<Rightarrow> bool) \<times> 'e set \<times> 'f pupdate) \<times> 'd" shows "source (a, b) = a"
path_head: shows "path AB ([w] || [(r1, r2)]) (p1, p2)"
zip_append: fixes xs :: "'b list"   and us :: "'c list"   and ys :: "'b list"   and vs :: "'c list" assumes "length xs = length us" shows "zip (xs @ ys) (us @ vs) = zip xs us @ zip ys vs"
lin_data_in': shows "linearize data_in' = filter (\<lambda>(t, X). enat (nt - t) \<le> right I) (linearize data_in)"
IH: shows "\<exists>d>0. \<forall>x\<in>S. x \<noteq> a \<longrightarrow> d \<le> dist a x"
is_renaming_list_def: fixes \<sigma>s :: "'s list" shows "is_renaming_list \<sigma>s = Ball (set \<sigma>s) is_renaming"
radical_eq_0_iff: fixes x :: "'a" shows "(radical x = (0::'a)) = (x = (0::'a))"
set_intros_2: fixes y :: "'a"   and x22 :: "'a list"   and x21 :: "'a" assumes "y \<in> set x22" shows "y \<in> set (x21 \<Colon> x22)"
sep_conj_true_P: fixes P :: "'a \<Rightarrow> bool" shows "((\<lambda>s. True) \<and>* (\<lambda>s. True) \<and>* P) = ((\<lambda>s. True) \<and>* P)"
weak_transition_weakI: fixes P :: "'state"   and Q :: "'state"   and \<alpha> :: "('act, 'pred) S_action"   and Q' :: "'state"   and P' :: "'state" assumes "P \<Rightarrow>\<^sub>S Q"   and "Q \<Rightarrow>\<langle>\<alpha>\<rangle>\<^sub>S Q'"   and "Q' \<Rightarrow>\<^sub>S P'" shows "P \<Rightarrow>\<langle>\<alpha>\<rangle>\<^sub>S P'"
dist_Bonk_Schramm_extension_def: shows "dist \<equiv> map_fun rep_Bonk_Schramm_extension (map_fun rep_Bonk_Schramm_extension id) extended_distance"
integral_sin_and_cos_1: fixes m :: "int"   and n :: "int" shows "LINT x|lebesgue_on {- pi..pi}. cos (real_of_int m * x) * cos (real_of_int n * x) = (if \<bar>m\<bar> = \<bar>n\<bar> then if n = 0 then 2 * pi else pi else 0)"
t_in_ts: fixes i :: "nat" assumes "i < k" shows "ts ! i \<in> set ts"
row_def: fixes A :: "'a Matrix.mat"   and i :: "nat" shows "Matrix.row A i = Matrix.vec (dim_col A) (\<lambda>j. A $$ (i, j))"
invertible_def: fixes u :: "('a set \<times> 'b) set" assumes "u \<in> carrier_direct_lim" shows "invertible u = (\<exists>v\<in>carrier_direct_lim. add_rel u v = \<lfloor>U, \<zero>\<^bsub>U\<^esub>\<rfloor> \<and> add_rel v u = \<lfloor>U, \<zero>\<^bsub>U\<^esub>\<rfloor>)"
less_diff_eq: fixes plus :: "'d \<Rightarrow> 'd \<Rightarrow> 'd"   and zero :: "'d"   and minus :: "'d \<Rightarrow> 'd \<Rightarrow> 'd"   and uminus :: "'d \<Rightarrow> 'd"   and less_eq :: "'d \<Rightarrow> 'd \<Rightarrow> bool"   and less :: "'d \<Rightarrow> 'd \<Rightarrow> bool"   and a :: "'d"   and c :: "'d"   and b :: "'d" assumes "class.ordered_ab_group_add plus zero minus uminus less_eq less" shows "less a (minus c b) = less (plus a b) c"
locate_b_2_a: fixes as :: "nat"   and am :: "nat list"   and q :: "nat"   and aaa :: "cell list"   and xs :: "cell list"   and ires :: "cell list" assumes "inv_locate_b (as, am) (q, aaa, Bk # xs) ires" shows "inv_locate_a (as, am) (Suc q, Bk # aaa, xs) ires"
open_halfspace_lt: fixes a :: "'a"   and b :: "real" shows "open {x. a \<bullet> x < b}"
asEnv_def: fixes qrho :: "'d \<Rightarrow> 'e \<Rightarrow> ('f, 'g, 'varSort, 'var, 'h) qTerm option" shows "asEnv qrho \<equiv> \<lambda>xs. lift asTerm (qrho xs)"
mem_grow_size: fixes m :: "mem"   and n :: "nat"   and m' :: "mem" assumes "mem_grow m n = m'" shows "mem_size m + 64000 * n = mem_size m'"
UP_map\<^sub>0_obj: fixes V\<^sub>B :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and H\<^sub>B :: "'b \<Rightarrow> 'b \<Rightarrow> 'b"   and \<a>\<^sub>B :: "'b \<Rightarrow> 'b \<Rightarrow> 'b \<Rightarrow> 'b"   and \<i>\<^sub>B :: "'b \<Rightarrow> 'b"   and src\<^sub>B :: "'b \<Rightarrow> 'b"   and trg\<^sub>B :: "'b \<Rightarrow> 'b"   and a :: "'b" assumes "strictified_bicategory V\<^sub>B H\<^sub>B \<a>\<^sub>B \<i>\<^sub>B src\<^sub>B trg\<^sub>B"   and "horizontal_homs.obj V\<^sub>B src\<^sub>B a" shows "weak_arrow_of_homs.map\<^sub>0 (strictified_bicategory.src V\<^sub>B H\<^sub>B \<a>\<^sub>B \<i>\<^sub>B src\<^sub>B trg\<^sub>B) (strictified_bicategory.UP V\<^sub>B H\<^sub>B \<a>\<^sub>B \<i>\<^sub>B src\<^sub>B trg\<^sub>B) a = strictified_bicategory.UP\<^sub>0 V\<^sub>B H\<^sub>B \<a>\<^sub>B \<i>\<^sub>B src\<^sub>B trg\<^sub>B a"
assoc_in_hom'_1: fixes \<mu> :: "'d"   and \<nu> :: "'d"   and \<tau> :: "'d" assumes "D.arr \<mu>"   and "D.arr \<nu>"   and "D.arr \<tau>"   and "src\<^sub>D \<mu> = trg\<^sub>D \<nu>"   and "src\<^sub>D \<nu> = trg\<^sub>D \<tau>" shows "\<guillemotleft>\<a>\<^sub>D[\<mu>, \<nu>, \<tau>] : src\<^sub>D \<tau> \<rightarrow>\<^sub>D trg\<^sub>D \<mu>\<guillemotright>"
diff_ge_divisor_imp_sub_mod_less: fixes x :: "nat"   and y :: "nat"   and m :: "nat" assumes "x \<le> y"   and "m \<le> y - x"   and "0 < m" shows "x < y - (y - x) mod m"
d0_def: shows "ps2_P.d0 = prod_list ps2_P.dims0"
BRBangCases': fixes P :: "pi"   and Q :: "pi"   and Rel :: "(pi \<times> pi) set" assumes "(P, !Q) \<in> bangRel Rel" obtains P :: "pi" and Qa :: "pi" where "Pa__ = !P" and "!Q = !Qa" and "(P, Qa) \<in> Rel"
tab_simps_5: shows "cod \<mu> = u \<star> u\<^sub>0"
implc_get_offending_flows_simp_rule: fixes G :: "'a list_graph"   and X :: "('a \<times> 'a) set" assumes "wf_list_graph G" shows "(\<forall>F\<in>set (implc_get_offending_flows (TopoS_Composition_Theory_impl.get_ACS (get_impl M)) G). set F \<subseteq> X) = (\<forall>F\<in>get_offending_flows (TopoS_Composition_Theory.get_ACS (get_spec M)) (list_graph_to_graph G). F \<subseteq> X)"
cod_char: fixes f :: "(bool, unit) J.arr" shows "J.cod f = (if J.arr f then J.MkIde (J.Cod f) else J.null)"
assign_val: fixes A :: "'b set"   and H :: "(('c, 'b) fm list \<times> 'b) set"   and a :: "'b"   and x :: "'c"   and i :: "'b" assumes "Hintikka A H"   and "Pro x at a in' H"   and "(\<^bold>\<not> Pro x) at i in' H"   and "a \<in> assign A H i"   and "i \<in> names H" shows "False"
content_gcd_primitive_2: fixes f :: "'b poly"   and g :: "'b poly" assumes "f \<noteq> 0" shows "content (gcd (primitive_part f) (primitive_part g)) = (1::'b)"
simps_9: fixes x1 :: "'a" shows "Stuck \<noteq> Normal x1"
map_inj_on: fixes f :: "'c \<Rightarrow> 'b"   and xs :: "'c list"   and ys :: "'c list" assumes "map f xs = map f ys"   and "inj_on f (set xs \<union> set ys)" shows "xs = ys"
lenext_singleton: fixes gts :: "'b list \<Rightarrow> 'b list \<Rightarrow> bool"   and y :: "'b"   and x :: "'b" shows "lenext gts [y] [x] = gts [y] [x]"
monom_mult_pprod_def: shows "monom_mult_pprod = pprod.monom_mult"
subcls1_induct_aux: fixes P :: "(char list \<times> char list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> 'b) list) list"   and C :: "char list"   and wf_md :: "(char list \<times> char list \<times> (char list \<times> ty) list \<times> (char list \<times> ty list \<times> ty \<times> 'b) list) list \<Rightarrow> char list \<Rightarrow> char list \<times> ty list \<times> ty \<times> 'b \<Rightarrow> bool"   and Q :: "char list \<Rightarrow> bool" assumes "is_class P C"   and "wf_prog wf_md P"   and "Q Object"   and "\<And>C D fs ms. \<lbrakk>C \<noteq> Object; is_class P C; class P C = \<lfloor>(D, fs, ms)\<rfloor> \<and> wf_cdecl wf_md P (C, D, fs, ms) \<and> P \<turnstile> C \<prec>\<^sup>1 D \<and> is_class P D \<and> Q D\<rbrakk> \<Longrightarrow> Q C" shows "Q C"
assms_2: shows "T \<subseteq> S \<times> S"
G_eq: fixes x :: "real"   and n :: "nat" assumes "x \<in> {0<..1}" shows "G (real n + x) = Gamma (real n + x)"
pos_oriented_opposite_ocircline: fixes H :: "ocircline" shows "pos_oriented (opposite_ocircline H) = (\<not> pos_oriented H)"
diff_le_eq: fixes plus :: "'c \<Rightarrow> 'c \<Rightarrow> 'c"   and zero :: "'c"   and minus :: "'c \<Rightarrow> 'c \<Rightarrow> 'c"   and uminus :: "'c \<Rightarrow> 'c"   and less_eq :: "'c \<Rightarrow> 'c \<Rightarrow> bool"   and less :: "'c \<Rightarrow> 'c \<Rightarrow> bool"   and a :: "'c"   and b :: "'c"   and c :: "'c" assumes "class.ordered_ab_group_add plus zero minus uminus less_eq less" shows "less_eq (minus a b) c = less_eq a (plus c b)"
islimpt_punctured: fixes x :: "'b"   and S :: "'b set" shows "x islimpt S = x islimpt S - {x}"
path_strategies_good: fixes P :: "'a llist"   and n :: "nat" assumes "lset P \<subseteq> S"   and "enat n < llength P" shows "path_strategies P $ n \<in> good (P $ n)"
STL3: fixes F :: "(nat \<Rightarrow> 'b) \<Rightarrow> bool" shows "\<turnstile> \<box>\<box>F = \<box>F"
continuous_on_closed_Collect_le: fixes s :: "'c set"   and f :: "'c \<Rightarrow> real"   and g :: "'c \<Rightarrow> real" assumes "continuous_on s f"   and "continuous_on s g"   and "closed s" shows "closed {x \<in> s. f x \<le> g x}"
lsumr_rsuml: fixes x :: "('h + 'i) + 'j" shows "lsumr (rsuml x) = x"
poly_of_vec_finsum: fixes f :: "'a \<Rightarrow> rat vec"   and X :: "'a set" assumes "f \<in> X \<rightarrow> Rn" shows "poly_of_vec (finsum gs.V f X) = (\<Sum>i\<in>X. poly_of_vec (f i))"
zero_hmem_one: fixes x :: "hf" shows "(x \<^bold>\<in> 1) = (x = 0)"
\<Lambda>_PBD_axioms: shows "\<Lambda>_PBD \<V> \<B> 1 {\<k>}"
one_plus_star: fixes x :: "'a" shows "x\<^sup>\<star> = ((1::'a) + x)\<^sup>\<star>"
AsGuardExpr: fixes \<Gamma> :: "'d \<Rightarrow> ('e, 'd, 'f) com option"   and \<Theta> :: "'d \<Rightarrow> ('e, 'd, 'f) ann list option"   and Q :: "'e set"   and A :: "'e set"   and p :: "('e, 'd, 'f) ann"   and e :: "('e, 'd, 'f) com"   and a :: "'e set"   and r :: "'e set"   and f :: "'f"   and b :: "'e set" assumes "assertionsR \<Gamma> \<Theta> Q A p e a" shows "assertionsR \<Gamma> \<Theta> Q A (AnnRec r p) (Guard f b e) a"
approx_mult_subst2: fixes u :: "'a star"   and x :: "'a star"   and v :: "'a star"   and y :: "'a star" assumes "u \<approx> x * v"   and "x \<approx> y"   and "v \<in> HFinite" shows "u \<approx> y * v"
zero_fun: fixes x :: "'d" shows "0 x = (0::'c)"
step: fixes name :: "name"   and rs :: "(Term_Class.term list \<times> pterm) fset"   and irs :: "(name \<times> (Term_Class.term list \<times> pterm) fset) fset"   and pats :: "Term_Class.term list"   and rhs :: "pterm"   and t :: "pterm"   and t' :: "pterm" assumes "(name, rs) |\<in>| irs"   and "(pats, rhs) |\<in>| rs"   and "name, pats, rhs \<turnstile>\<^sub>i t \<rightarrow> t'" shows "irs \<turnstile>\<^sub>i t \<longrightarrow> t'"
w1_2: shows "w1 \<subseteq> fst ux"
top_mult_annil: fixes x :: "'a" shows "\<top> \<cdot> x = \<top>"
unique_prepression5_0: fixes H :: "'a set"   and f :: "nat \<Rightarrow> 'a"   and n :: "nat"   and s :: "nat \<Rightarrow> 'b"   and g :: "nat \<Rightarrow> 'a"   and m :: "nat"   and t :: "nat \<Rightarrow> 'b" assumes "free_generator R M H"   and "f \<in> {j. j \<le> n} \<rightarrow> H"   and "inj_on f {j. j \<le> n}"   and "s \<in> {j. j \<le> n} \<rightarrow> carrier R"   and "g \<in> {j. j \<le> m} \<rightarrow> H"   and "inj_on g {j. j \<le> m}"   and "t \<in> {j. j \<le> m} \<rightarrow> carrier R"   and "l_comb R M n s f = l_comb R M m t g"   and "\<forall>j\<le>n. s j \<noteq> \<zero>\<^bsub>R\<^esub>"   and "\<forall>k\<le>m. t k \<noteq> \<zero>\<^bsub>R\<^esub>"   and "f n \<notin> g ` {j. j \<le> m}"   and "0 < n" shows "False"
l3: shows "- (ordinate A - ordinate B) * abscissa X + (abscissa A - abscissa B) * ordinate X = - abscissa A * (ordinate A - ordinate B) + ordinate A * (abscissa A - abscissa B)"
assms_3: fixes u :: "'a"   and v :: "'b" assumes "u \<in> basisA"   and "v \<in> basisB" shows "v \<bullet>\<^sub>C (F *\<^sub>V u) = v \<bullet>\<^sub>C (G *\<^sub>V u)"
valid_Entry_path_ascending_path: fixes sourcenode :: "'a \<Rightarrow> 'b"   and targetnode :: "'a \<Rightarrow> 'b"   and kind :: "'a \<Rightarrow> ('c, 'd, 'e, 'f) edge_kind"   and valid_edge :: "'a \<Rightarrow> bool"   and Entry :: "'b"   and get_proc :: "'b \<Rightarrow> 'f"   and get_return_edges :: "'a \<Rightarrow> 'a set"   and procs :: "('f \<times> 'c list \<times> 'c list) list"   and Main :: "'f"   and as :: "'a list"   and n :: "'b" assumes "CFG sourcenode targetnode kind valid_edge Entry get_proc get_return_edges procs Main"   and "CFG.valid_path' sourcenode targetnode kind valid_edge get_return_edges Entry as n" obtains as' :: "'a list" where "CFG.valid_path' sourcenode targetnode kind valid_edge get_return_edges Entry as' n" and "set (CFG.sourcenodes sourcenode as') \<subseteq> set (CFG.sourcenodes sourcenode as)" and "\<forall>a'\<in>set as'. intra_kind (kind a') \<or> (\<exists>Q r p fs. kind a' = Q:r\<hookrightarrow>\<^bsub>p\<^esub>fs)"
hyps: shows "FWNormalisationCore.sorted p l \<longrightarrow> all_in_list p l \<longrightarrow> distinct p \<longrightarrow> allNetsDistinct p \<longrightarrow> singleCombinators p \<longrightarrow> wellformed_policy2Pr p"