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Theory Cardinal
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/FOL/ZF/Cardinal.html23 May 2024: b B⟧ cons(a,A)b,B)" apply (unfoldapply (rule_tac x = "λycons (a,A). ... B; a A; b B⟧ cons(a,A)b,B)" by (simp add:lemma cons_lepoll_cons_iff: "⟦a A; b B⟧ cons(a,A)b,B) A B" by (blast -
Theory RBT
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Library/RBT.html23 May 2024: lift_definition bulkload :: "('a::b) list ('a, 'b) rbt" is "rbt_bulkload". lift_definition map_entry :: "'a ('b 'b) ('a::linorder, 'b) rbt ('a, 'b) rbt" is rbt_map_entry by ... lift_definition combine_with_key :: "('a 'b 'b 'b) ('a::linorder, 'b) rbt ('a, -
Theory HOL.Finite_Set
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Proofs/HOL.Finite_Set.html23 May 2024: f y g)" by (simp add:end inductive fold_graph :: "('a 'b 'b) 'b 'a set 'b bool" for f :: "'a 'b 'b" and z :: 'b where emptyI [intro]: "fold_graph ... that by auto definition fold :: "('a 'b 'b) 'b 'a set 'b" where "fold f z AA then (THE y. -
Theory Elementary_Topology
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Analysis/Elementary_Topology.html23 May 2024: finite b b B}. B') = k" by auto then obtain k where "kaK. ... finite b b B}. B')K" by (intro exI[of _ "kK)"]) auto next case (Basis S) then show? -
Theory OrderType
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/FOL/ZF/OrderType.html23 May 2024: def) done lemma pred_Inr_bij: "b B id(AB,b,s))AB,b,s), pred(AB, Inr(b), radd(A,r,B,s)))" unfoldingapply (rule_tac d = "λz. ... z" indone lemma ordertype_pred_Inr_eq: "⟦b B; well_ord(A,r); well_ord(B,s)⟧AB, Inr(b), radd(A,r,B,s)), -
Theory Porder
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOLCF/Porder.html23 May 2024: notation (ASCII) not_below (infix "<<" 50) lemma below_eq_trans: "a b b = c a c" by (lemma eq_below_trans: "a = b b c a c" by (end class po = ... S <<| x)" end syntax (ASCII) "_BLub" :: "[pttrn, 'a set, 'b] 'b" ("(3LUB _:_./ _)" [0,0, 10] 10) syntax -
Theory DefiniteAssignment
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Bali/DefiniteAssignment.html23 May 2024: UNIV)" bynote B' = ‹B B'› withshow? case by auto next case CondOr thus? ... UNIV)" by (elimsimp add: inj_term_simps) ( inj_term_simps needed to handle wt (defined without ⟨⟩) ) note B' = ‹B B'› withshow? -
Theory Tests
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Eisbach/Tests.html23 May 2024: A x y Q) (a b. B (a :: 'a) (b :: 'a) Q) (x y. ... A x B" "x. A x" assume Y: "A B" have "B B B B B B" apply (intro conjI) apply (in H[OF X(2)]:"x. -
Theory Record
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/Record.html23 May 2024: iso_tuple_fst_update :: "('a, 'b, 'c) tuple_isomorphism ('b 'b) ('a 'a)" where "iso_tuple_fst_update isom fisomfisom" definition iso_tuple_snd_update :: "('a, 'b, 'c) tuple_isomorphism ('c ... b 'b) ('a 'a)) ('a 'b) bool" where -
Theory Order_Relation
https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/Order_Relation.html23 May 2024: b" "(b, a) r" proof - from that have "br a" unfolding underS_def by blast with have "br b" by blast then show? ... b, a) r phi b) phi a" define chi where "chi b (b, a) r phi b" for b with have "wf (R a)" by auto then have "(bc.
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