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23 May 2024: subset.chain 𝒜 𝒞 = (𝒞 𝒜 (X𝒞. Y𝒞. X Y Y X))" by (auto simp: subset.chain_def) lemma subset_chain_insert: "subset.chain 𝒜 (insert B ) B 𝒜 (X. ... S" and 2: "AC. BC. A B B A" for C proof - let?

23 May 2024: simp lemma set_mset_empty [simp]: "by (simp add: set_mset_def) lemma set_mset_single: "set_mset {#b#} = {b}" by (simp add: set_mset_def) lemma ... Mx A" by (where x = "Mx#}"]) simp lemma multiset_add_sub_el_shuffle: assumes "c # B" and "b c" shows

23 May 2024: c)(Split(d))" definition List_rec :: "['a item, 'b, ['a item, 'a item, 'b]=>'b] => 'b" where "List_rec M c dg. ... ML ) list_rec :: "['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b" where "list_rec l c dl) c (%x y r.

23 May 2024: iff: "principal a = principal b a b b a" unfolding po_eq_conv [where 'a='b] principal_below_iff. ... principal a = Abs {b. b a}" assumes countable: "f::'af" shows "ideal_completion r principal Rep" proof interpret type_definition Rep Abs "{S.

23 May 2024: assumes "bound0 p" shows "Ifm bbs (b # bs) pbbs (b' # bs) p" usingwhere b="b" and bs="bs" and b'="b'"] by (induct p rule:simp add: gr0_conv_Suc) fun ... I': "numbound0 a Inum (b#bs) (numsubst0 a t)b'#bs) a)#bs) t" by (induct t rule:simp:where b="b" and b'

23 May 2024: bB. x b j) (x = t) (x - D = t))" "⟦Dt B⟧ ((x::jD}. ... bB. x b j) (x t) (x - D t))" "⟦Dt B⟧ ((x::jD}.

23 May 2024: locale semigroup = fixes f :: "'a 'a 'a" (infixl "" 70) assumes assoc [ac_simps]: "a b c = a (b c)" locale abel_semigroup = semigroup assumes commute [ac_simps]: "a b = b a" ... standard (fact add_assoc) declareend hide_fact add_assoc class

23 May 2024: ASCII) "_sum_list" :: "pttrn => 'a list => 'b => 'b" ("(3SUM _<-_. _)" [0, 51, 10] 10) syntax "_sum_list" :: "pttrn => 'a list => 'b => 'b" ("(3__. _)" ... b" ("(3PROD _<-_. _)" [0, 51, 10] 10) syntax "_prod_list" :: "pttrn => 'a list => 'b => 'b" ("(3__.

23 May 2024: assumes group_hom: "group_hom G (BijGroup E) φ" definition orbit :: "[_, 'a 'b 'b, 'b] 'b set" where "orbit G φ x = {(φ g) x | g. ... x E}" definition stabilizer :: "[_, 'a 'b 'b, 'b] 'a set" where "stabilizer G φ x = {g carrier G. (

23 May 2024: A a u B b) apply (case_tac "A = B") apply simp apply simp apply (apply clarify apply (rename_tac A a u B b) apply (case_tac "A = B") apply ... rotate_tac -1) apply simp apply (rotate_tac -1) apply (case_tac "B = C") apply simp apply (rotate_tac -1) apply