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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: 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

23 Feb 2024: pathway CD4 T cell alloresponses’/em.b/b/p pThe Patey prize celebrates the work of David Patey (1899-1977), a distinguished surgeon at the Middlesex Hospital who gained international recognition ... call for abstracts/bbfor early career

23 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.

23 Feb 2024: GR.</b>2020 (accepted)<b></b><i>Life Science Alliance</i>.</li> </ol> <ol start="2" type="1"> <li>Developing Therapies for Neurodegenerative Disorders: Insights from Protein Aggregation and Cellular Stress ... Responses.<b>Mallucci GR</b>, Klenerman D,

23 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?

23 Feb 2024: pathway CD4 T cell alloresponses’/em.b/b/p pThe Patey prize celebrates the work of David Patey (1899-1977), a distinguished surgeon at the Middlesex Hospital who gained international recognition

23 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.

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.

23 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?

23 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.

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: 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: ng ((n2)) sums x" using sums_if'[OF ‹g sums x›]. have if_eq: "B T E. ... xa <.< b} ya <.< bf x n - f y nL nx - y" shows "DERIV (λ x.

23 Feb 2024: Concentrations of the Stress Hormone Copeptin increase upon Hypoglycaemia in Patients with Type 1 Diabetes dependent of Hypoglycaemia Awareness.<b> </b><i>PLoS One. ... and <b>Brindle, K. M.</b> (2014) <i>Contrast Media and Mol. Imag.</i> <b>9</b><b>,</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: thesis using rel_interior_sing by auto next case False obtain B where B: "independent B B S SBBS" using basis_exists[of S] by metis then have "Busing‹S› ... empty by auto have "BB" using subspace_span[of B] subspace_0[of "span B"] span_superset by

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: 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: 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.