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23 May 2024: Ax B' B' B)" apply (case_tac "x A") apply (apply (rule_tac x = "A - {x}" in exI) apply fast done abbreviation nat3 :: nat ("3") where "3 Suc 2" abbreviation nat4 :: ... P (f b))" by auto subsubsection "sums" notation case_sum (infixr "'(')" 80) primrec

23 Feb 2024: 2015). Inhibition of UDP-glucosylceramide synthase in mice prevents Gaucher disease-associated B cell malignancy. ... b(2013). The legal u00a0imperative for treating rare disorders. bOrphanet Journal of Rare Diseases.

23 May 2024: b F} = {a b |b. b = x b F}" by blast have "a (xF) = a x aF" by (simp add: inf_sup_distrib1) also have ". = a xa b |b. b F}" ... by simp also have ". a b |b. b = x b F}" by (unfold Sup_insert[THEN sym], simp) finally show "a (xF)a b |b.

23 May 2024: a band a: "a = a'a b" and b: "b = b'a b" shows "coprime a' b'" proof - from c have "abby simp with div_gcd_coprime have "coprime (aa b) ... a = a'a b b = b'a ba' b'" proof - have "coprime (aa b) (ba b)" usingby auto then show?

23 May 2024: B B'B'B'lemma assumes B: "independent B" shows extend_basis_superset: "BB" and independent_extend_basis: "B)" and span_extend_basis[simp]: "B)proof - define p where "p B' ... B B'B'B'for B' obtain B' where "p B'" using

23 May 2024: and (Haskell) infixr 9 "." subsection ‹The Forward Composition Operator ‹fcomp›› definition fcomp :: "('a 'b) ('b 'c) 'a 'c" (infixl ">" 60) where "f > g = (λx.

23 May 2024: a B b B xB. F xF a) (F b)) eventually P (bB. ... F. B) B" unfoldingby (force intro: eventually_True) lemma prod_filter_INF: assumes "Iand "Jshows "(iI.

23 May 2024: B AA)" proof safe fix B assume B: "B Ashow "A)" unfolding inj_on_def by (next assume "A)" from vec.linear_injective_left_inverse[OFobtain g where "g" and "gAby ... A unfolding invertible_def by blast obtain B' where BB': "B B'and B'B: "B' Busing inv_B

23 May 2024: a'' b'" by auto also have "b (a'' b') = b' (a'' b)" by simp finally have "b' (a b'') = b' (a'' b)". ... a = "aa b" let? b = "ba b" from b have "?ba b = b" by simp with b have "?bby fastforce withhave q2: "qa?

4 Jun 2024: Venue: Council Room, Murray Edwards College (meet at porter’s lodge at 2pm for a 2:15pm start)/div divb/b/div divbiLiteraryspan class="markl40ibvki8" data-markjs="true" data-ogac="" ... There are a few spaces remaining, so please do sign up if you are

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 May 2024: R v bby (intro finite_subset[OF ]) simp_all have "(b |? R u b -? R v b) s b) = (b{b? R u bb? R v bR u b -? R v ... b) s b)" by (introalso have ". = (b{b? R u bb? R v bR u b s b) - (b{b?

22 Feb 2024: Part B continued. If you answered “no”, please indicate (why you are especially deserving of a Christ’s College International Award.

23 May 2024: aba $< b | b $ #0) P(a, #2 $ b)⟧ P(a,b)" shows "P(u,v)" apply (subgoal_tac "(λ⟨x,y⟩. ... ab0 $ a $+ b | b $ #0) P(a, #2 $ b)⟧ P(a,b)" shows "P(u,v)" apply (subgoal_tac " (λ⟨x,y⟩.

23 May 2024: case using A by (auto simp:intro!: bexI[where x="λi. f i g i"]) next case (UN B) then obtain b where "x b" "b B" by auto hence ... A. a b" using UN by simp thus? case using ‹b B› by (next case (Basis s) then obtain a b where xs: "xa b" "sa b" "i.

23 Feb 2024: S, Machado RD, Mueller M, Kinzel B, Yung LM, <b>Wilkinson JM</b>, Moore SD, Drake KM, Aldred MA, Yu PB, Upton PD, Morrell NW. ... Wilkinson</b><b> JM</b>, Davidson RK, Swingler TE, Jones ER, Corps AN, Johnston P, Riley GP, Chojnowski AJ, Clark IM <a href=

23 May 2024: definition SIM :: "[where "SIM(t,t',R) == (tt'tt'a a' b b'. ... rews => fn ctxt => SIMPLE_METHOD' (inj_rl_tac ctxt rews)) › lemma ccl_injs: "<a,ba',b'a=a' b=b')" "b b'.

23 May 2024: thesis by auto next case False from ‹a dvd b› obtain c where b: "b = a c". ... b b" by simp then have "normalize aa div b b)" by simp then show?

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: 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.