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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.