hcju/isabelleps huggingface dataset:
sum_list_nlex_eq_zeroI: fixes xs :: "(real \<times> real) list"   and x :: "real \<times> real" assumes "list_all (\<lambda>x. Counterclockwise_2D_Arbitrary.lex x 0) xs"   and "sum_list xs = 0"   and "x \<in> set xs" shows "x = 0"
ide_char: fixes f :: "('o, 'a) arr" shows "ide f = (f \<noteq> Null \<and> Dom f \<in> Obj \<and> Cod f = Dom f \<and> Map f = Id (Dom f))"
filterlim_mono: fixes f :: "'a \<Rightarrow> 'c"   and F2 :: "'c filter"   and F1 :: "'a filter"   and F2' :: "'c filter"   and F1' :: "'a filter" assumes "filterlim f F2 F1"   and "F2 \<le> F2'"   and "F1' \<le> F1" shows "filterlim f F2' F1'"
Bounded_Hypergraph_axioms: shows "Bounded_Hypergraph E k"
smap_def: fixes x :: "'w set" shows "dual_order.poset_simplex_map \<P> x = {y. dual_order.pseudominimal_in (dual_order.below_in \<P> x) y}"
deg_belowI: fixes n :: "nat"   and p :: "nat \<Rightarrow> 'a" assumes "n \<noteq> 0 \<Longrightarrow> coeff P p n \<noteq> \<zero>"   and "p \<in> carrier P" shows "n \<le> deg R p"
eq_implies_ltl_equiv: fixes \<phi> :: "'a ltln"   and \<psi> :: "'a ltln"   and w :: "nat \<Rightarrow> 'a set" assumes "\<phi> \<sim> \<psi>" shows "w \<Turnstile>\<^sub>n \<phi> = w \<Turnstile>\<^sub>n \<psi>"
par_comp\<^sub>l\<^sub>s\<^sub>s\<^sub>t_split_1: fixes A :: "('lbl strand_label \<times> ('fun, 'var) stateful_strand_step) list"   and B :: "('lbl strand_label \<times> ('fun, 'var) stateful_strand_step) list"   and Sec :: "('fun, 'var) Term.term set" assumes "par_comp\<^sub>l\<^sub>s\<^sub>s\<^sub>t (A @ B) Sec" shows "par_comp\<^sub>l\<^sub>s\<^sub>s\<^sub>t A Sec"
cblinfun_scaleC_left_def: shows "cblinfun_scaleC_left \<equiv> map_fun id CBlinfun (\<lambda>x y. y *\<^sub>C x)"