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23 May 2024: next assume "euclidean_size bshow "bproof (assume "bwith mod_size_less have "euclidean_size (b mod b)b". ... b dvd f a}› with ‹finite A› have ‹finite B› and ‹a B b dvd f a› for a by simp_all then have ‹(aB.

23 May 2024: simp]: "⟦b; b⟧ b m b n n m" using power_strict_decreasing [of m n b] by (auto intro:lemma power_strict_decreasing_iff [simp]: "⟦b; b⟧ b m < b ... le) qed lemma power_increasing_iff [simp]: "b b x b y x y" by (blast intro:less_imp_le) lemma

23 May 2024: fixes f::"_ _ :: {assumes [M f" "AM" "BM" and null: "(A - B) (B - A)M" shows "(x A. ... a (A - B) (B - A)" usingby blast then show "AE x in M.

23 May 2024: x A" and "Ashows "x A) = x F A" proof - from ‹A› obtain b where "b A" by blast then obtain B where : "Ab B" "b B" by (blast dest: ... a set 'b 'b" ("(3MAX __./ _)" [0, 0, 10] 10) translations "MIN x y.

23 May 2024: b' B (b, b') r" proof fix b' show "b' B (b, b') r" proof assume As: "b' B" hence : "br b'r" usingby auto fromhave "b' = b (b',b) r" ... by auto moreover have "b' = b (b, b') r" usingby (auto simp add: refl_on_def) moreover have "b' b (b',b) r (b,b') r"

23 May 2024: Pz = x) (Pz = y))" definition Let :: "'a ('a 'b) 'b" where "Let s f f s" translations "_Let (_binds b bs) e" "_Let b (_Let bs e)" "let x = a in ... lemma not_sym: "t s s t" by (erule contrapos_nn) (erule sym) lemma eq_neq_eq_imp_neq: "⟦x = a; a b; b =

23 May 2024: A = B; B = C⟧ A = C" and trans_elem: "a b c A. ... A type; b : B⟧ inr(b) : AB" and PlusI_inrL: "b d A B.

23 May 2024: session key and various verifiers) | SR7: "⟦ evs7 sr; Nonce Nbevs7;B); BKNb,pairK(A,B)); Key Kevs7; Inputs B (Card B) ⦃Agent A, Nonce Na⦄evs7⟧B) B ⦃Nonce Nb, Key ... lemma Confidentiality_B: "⟦B) B ⦃Nonce Nb, Key K, Certificate,A,B)) (Nonce

23 May 2024: thesis by (simp add:qed theorem n_subsets: assumes "finite A" shows "card {B. ... g? B? B'" apply (where f' = "λl. (ll"]) using assms by (auto simp: 2 simp flip: length_0_conv intro!: 3) have fin: "finite {xs.

23 May 2024: bvusing ‹T› by auto have [simp]: " T {v. bvusing ‹norm b› ‹b T› by auto define f where "f λx. ... R. ba} (- U)for a::'a and b::'b by force have : "r.

23 May 2024: B; u A; v B⟧ A B" by (lemma insert_lepoll_cong: assumes "A B" "b B" shows "insert a Ab B" proof - obtain f where f: "inj_on f A" ... where "inj_on f A" "f A B" using assms by (then obtain b where b: "b B" "b f A" by auto show?

23 May 2024: apply (fast intro!: FiniteFun.intros) done lemma FiniteFun_subset: "⟦c<=b; b A-||>B⟧ c A-||>B" by (blast intro: FiniteFun_subset_lemma) ( Some further results by Sidi O. ... f A->B f A-||>B" apply (erule Fin.induct) apply (simp add:apply (case_tac "a

23 May 2024: case by (auto intro!: exI[of _ "min a b"]) next case UN then show? ... Q b b < a" and P: "eventually P at_top" shows "filterlim fa)" proof - from P obtain x where x: "y.

30 Apr 2024: Alternatively, you can book a hotel or B&B room via the Visit Cambridge website or visit the Cambridge Rooms site that includes accommodation at other Colleges.

23 May 2024: a = x) = a" by blast subsection‹Conditional Terms: ‹if-then-else›› lemma if_true [simp]: "(a else b) = a" by (unfoldlemma if_false [simp]: "(a else b) = b" by (unfoldNever use ... lemma misc_simps [simp]: "A = A" "AA" "AAAAA" "b,A)) = bA)" "({b})

23 May 2024: thesis. qed lemma sigma_sets_UNION: "countable B (b. b B bX A) BX A" using from_nat_into [of B] range_from_nat_into [of B] sigma_sets.Union [of ... a A aM B" assumes B: "b. b B bM A" shows "sigma_sets M AM B" proof (introfix a assume "aM A" fromshow "aM B

23 May 2024: lemma SigmaD1: "(a, b)A B a A" by blast lemma SigmaD2: "(a, b)A B b B a" by blast lemma SigmaE2: "(a, b)A B (a A b B ... j). (j, i)) (A B) = B A" by (auto simp add: set_eq_iff) lemma image_split_eq_Sigma: "(λx.

23 May 2024: b T j (i b) = b" "b. b T i b S" assumes eq: "a. ... b T - T' j (i b) = b" "b. b T - T' i b S - S'" assumes nn: "a.

23 May 2024: a = "aλb. (a b / (b b)). R. ... a b / (b b)). R.

23 May 2024: finally have "b<": "b r (a f b) f c". fromhave "c<": "c r (a f b) f c". ... also fromhave "… r a f …". finally have "b<": "b r a f (b f c)".