Search

23 May 2024: assumes "bound0 p" shows "Ifm bbs (b # bs) pbbs (b' # bs) p" usingwhere b="b" and bs="bs" and b'="b'"] by (induct p rule:simp add: gr0_conv_Suc) fun ... I': "numbound0 a Inum (b#bs) (numsubst0 a t)b'#bs) a)#bs) t" by (induct t rule:simp:where b="b" and b'

23 May 2024: c)(Split(d))" definition List_rec :: "['a item, 'b, ['a item, 'a item, 'b]=>'b] => 'b" where "List_rec M c dg. ... ML ) list_rec :: "['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b" where "list_rec l c dl) c (%x y r.

23 Feb 2024: 11),14878-14891.</p> <p><i>Heritability of Haemodynamics in the Ascending Aorta</i>.McGurk KA, Owen B,<b>Watson WD</b>, Nethonoda RM, Cordell HJ, Farrall M, Rider OJ, Watkins ... JJ, Sayeed RA, Petrou M, Krasopoulos G, Lake HA, Raman B,<b>Watson WD</b>,

3 May 2024: Now let Z_n be bin(n, p), independent of B which is Bernoulli ber(p). ... By the result of Exercise 3.6.5,. H(Z_n1) = H(Z_n B) >= H(Z_n B|B) = H(Z_n|B) = H(Z_n).

23 May 2024: ASCII) "_sum_list" :: "pttrn => 'a list => 'b => 'b" ("(3SUM _<-_. _)" [0, 51, 10] 10) syntax "_sum_list" :: "pttrn => 'a list => 'b => 'b" ("(3__. _)" ... b" ("(3PROD _<-_. _)" [0, 51, 10] 10) syntax "_prod_list" :: "pttrn => 'a list => 'b => 'b" ("(3__.

6 Dec 2023: Degree, as defined in the Regulations, to the M.B. or B.Chir. ... 1,350. 1,385. B.Th. Degree. 9,000. 9,250. Medical and Veterinary Degrees:. M.B., B.Chir.

23 May 2024: m adefinition ran :: "('a 'b) 'b set" where "ran m = {b. ... S'" hence 1: "dom m = A" by force hence 2: "ran m B" using ‹m?

23 May 2024: by blast lemma QSigmaD2: "<a;bA,B) b B(a)" by blast lemma QSigma_cong: "⟦A=A'; x. ... lemma QInrD: "QInr(b): A<>B b B" by blast ( <> is itself injective.

20 Mar 2024: 20. That Regulation 2(b) for the T. H. Middleton Fund (Statutes and Ordinances, p. ... Churchill in memory of her brother Dr Walter Myers, M.A., M.B., B.Chir., of Gonville and Caius College, and now known as the Walter Myers Fund, shall be used

23 May 2024: assumes group_hom: "group_hom G (BijGroup E) φ" definition orbit :: "[_, 'a 'b 'b, 'b] 'b set" where "orbit G φ x = {(φ g) x | g. ... x E}" definition stabilizer :: "[_, 'a 'b 'b, 'b] 'a set" where "stabilizer G φ x = {g carrier G. (

23 May 2024: A a u B b) apply (case_tac "A = B") apply simp apply simp apply (apply clarify apply (rename_tac A a u B b) apply (case_tac "A = B") apply ... rotate_tac -1) apply simp apply (rotate_tac -1) apply (case_tac "B = C") apply simp apply (rotate_tac -1) apply

23 May 2024: lemma wf_onI_pf: assumes "B. B A B R B Bshows "wf_on A R" unfolding wf_on_def proof (introfix P :: "'a bool" and x :: 'a let? ... a 'a) set ('b 'b) set (('a 'b) ('a 'b)) set" (infixr "<lex>" 80) where "ra <lex> rb = {((a, b), (a', b')).

23 May 2024: a, b], [b, b], [c, b], [a, c], [b, c], [c, c]]" by (simp add: eval_nat_numeral)} @{lemma "rotate1 [a,b,c,d] = [b,c,d,a]" by simp} @{lemma ... b 'b list 'b list" where "insort_insert_key f x xsf x fxs then xsf x xs)" abbreviation "sort sort_key (λx.

23 May 2024: bB. x b j) (x = t) (x - D = t))" "⟦Dt B⟧ ((x::jD}. ... bB. x b j) (x t) (x - D t))" "⟦Dt B⟧ ((x::jD}.

23 May 2024: based on the three cases of ordinals ) lemma transrec2_0 [simp]: "a,b) = a" by (THEN def_transrec, THEN trans], simp) lemma transrec2_succ [simp]: "i),a,b) = b(i, ... m),a,b) = b(m, rec(m,a,b))" unfolding rec_def apply (done lemma rec_type: "⟦na C(0);

23 May 2024: f (A <> B) (B <> A)" unfoldingby force thus? thesis using card_of_ordIso by blast qed lemma card_of_Plus_assoc: fixes A :: "'a set" and B :: "'b set" and C :: ... thesis using inj_on_iff_surj[of B "B A"]by blast qed (simp add: card_of_empty) lemma card_of

23 May 2024: zero [simp]: "begin subclass ring_1_no_zero_divisors proof fix a b :: 'a assume a: "aand b: "bshow "a bproof assume ab: "a bhence "a (a b)b" by simp ... thesis by (qed lemma division_ring_inverse_add: "ababa (a b)b" by (simp add: algebra_simps) lemma

23 May 2024: R. b" using assms by (auto simp: in_segment) have xb: "x b < b b" usingby auto assume "norm cc x" then have "c c (c - x) (c - x)" by (simp ... b = b a=b uby (smt (verit, best)lemma segment_degen_0: fixes a :: "'a :: real_vector" shows "(u).

23 May 2024: thesis usingof "top_of_set S" "top_of_set T" a b] by (qed moreover have "cλx. ... fst xxA) p" by (auto intro: continuous_on_subset [OF contp] simp:qed (force intro: continuous_intros) have ps1: "a b.

23 May 2024: pi f (rev pi x))" definition perm_bool :: "'xwhere "perm_bool pi b = b" definition perm_set :: "'x prm 'a set 'a set" where "perm_set pi X = {pi x | x. ... P b}b::'x. P b}" by auto ultimately show "infinite {b::'x.

23 May 2024: SesKeyevs); evs⟧ K=K' B=B' T=T'" apply (erule rev_mp) apply (erule rev_mp) apply (erule rev_mp) apply (eruleapply (frule_tac [7] Says_ticket_parts) apply (frule_tac ... lemma unique_CryptKey: "⟦B) ⦃Agent A, Agent B, Key SesKey, T⦄evs);B')

23 May 2024: B⟧ a B" by (auto simp add: explode_def) lemma explode_CartProd_eq: "a b) = (% (x,y). ... Z = "Upair a b" have "?Zby (simp add: Upair_nonEmpty) then have "xx?

23 Feb 2024: Wilkinson</b><b> JM</b>, Davidson RK, Swingler TE, Jones ER, Corps AN, Johnston P, Riley GP, Chojnowski AJ, Clark IM <a ... JM</b><b></b>, Marshall N, Tao H, Steel J, Lowen AC.

23 May 2024: aR" proof assume "carrier Ra" hence "a" by auto then obtain b where "bR" "a b" "b a" unfolding cgenideal_def using m_comm[OF assms] by auto thus "aR" using ... b Iφ a φ b" using phi_img_def by blast have "Ia" proof (assume "Ia" then obtain b where b:

23 Feb 2024: datatype="">antibody response</a></div><div class="field-item even"><a href="/subject/b-cell-receptor-bcr" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">B cell receptor ... WDF,</span><span>Hill</span><span>A,</span><b>Gupta</b><b

8 Nov 2023: Matthew Connelly, B.A., Columbia, Ph.D., Yale. Lalita Ramakrishnan, M.B.B.S., Baroda, Ph.D., Tufts. ... Janine Maegraith, B.A., M.A., Ph.D., Stuttgart. Events. Emmanuel College. Cambridge Seminars in the History of Cartography.

23 May 2024: l i<.<r i delta i})" proof (show "a'.b}" by (show "i. ... D (box l u) = (b?B. (u - l) b)" by (auto simp:symmetric]symmetric] intro!: prod.cong) qed simp lemma lborel_affine: fixes t :: "'a::euclidean_space" shows "cλx.

23 May 2024: simp]: "(vc t) = (v «| t)" by (cases t) auto lemma paint_rbt_less[simp]: "(paint c t |« v) = (t |« v)" by (cases t) auto fun rbt_ins :: "('a 'b 'b 'b) ... f k v t rule:end context ord begin definition rbt_insert_with_key :: "('a 'b 'b 'b) 'a 'b ('a,'b)

23 May 2024: P x)xP x)› by auto lemma verit_ite_simplify: ‹(B C) = B› ‹(B C) = C› ‹(If A' B B) = B› ‹(A') B C)A' C B)› ‹(If c (If c ... by auto lemmas verit_eq_simplify =lemma verit_minus_simplify: ‹(a :: 'a ::a› ‹(a :: 'a ::a› ‹b :: 'b :

23 May 2024: b 'b) ('a 'b 'b)" where F_strict: "F(and K: "K = (λh x y. ... a'b'b)") apply simp apply (simp split: COND_cases_iff) done end.

22 Feb 2024: This is a pragmatic step where doctors and nurses may not be available to visit all dying patients during the pandemic./b/span/span/div divspan style="font-family: ... serif;font-size: small"span style="font-size: medium"b/b/span/span/div divspan

23 May 2024: a. a A - b! b'. b' B - {b} a b'" using unique_class by fastforce next show "b'. ... b' B - {b} b' A - b" usingby fastforce qed lemma disjoint_sum: ‹contributor ‹Paulo Emílio de Vilhena›› "⟦ finite B; finite A; partition A B⟧ (bB.

23 May 2024: bot)" definition inl :: "where "inl(a) ==a>" definition inr :: "where "inr(b) ==b>" definition split :: "[where "split(t,f) == case(t,f, λu. ... inr"], ["bot","zero","succ"], ["bot","nil","cons"]]); › subsection ‹Rules for pre-order ‹[=››

23 May 2024: and g :: "'b 'a" and A :: "'a set" and B :: "'b set" assumes inj1: "inj_on f A" and sub1: "f A B" and inj2: "inj_on g B" and sub2: ... a: "a X" and b: "b A - X" for a b proof - from a have fa: "f a f X" by (from b have "g' b g' (A - X)" by (with

23 May 2024: i) b = f b" by (simp add: inner_sum_leftlemma (in euclidean_space) euclidean_eqI: assumes b: "b. ... b) = f" by (simp add: euclidean_representation_sum) lemma euclidean_isCont: assumes "b.

23 May 2024: LeafI: "Leaf(a) sexp" | NumbI: "Numb(i) sexp" | SconsI: "[| M sexp; N sexp |] ==> Scons M N sexp" definition sexp_case :: "['a=>'b, nat=>'b, ['a item, 'a item]=>'b, 'a item] => ... M, Scons M N), (N, Scons M N)})" definition sexp_rec :: "['a item, 'a=>'b,

12 Apr 2024: pounds}", "N{PLUS-MINUS SIGN}" = "$pm$", "N{NO-BREAK SPACE}" = "", "N{PARAGRAPH SEPARATOR}" = "nn", "N{GREEK CAPITAL LETTER ALPHA}" = 'A', "N{GREEK CAPITAL LETTER BETA}" = 'B', "N{GREEK CAPITAL LETTER GAMMA}" = ' ... APPLICATION}" = "", "N{MATHEMATICAL

23 May 2024: s" inductive_set setr :: "'a 'b 'b set" for s :: "'a 'b" where "sx x setr s" lemma sum_set_defs[code]: "λx. ... set fsts :: "'a 'b 'a set" for p :: "'a 'b" where "fst p fsts p" inductive_set snds :: "'a 'b 'b set" for p :: "'a 'b" where "snd p snds p"

23 May 2024: f x - g x) a - b) F" using tendsto_add [of f a F "λx. - ... norm (x y)xy K" using nonneg_bounded by blast obtain B where B: "B" and norm_g: "eventually (λx.

23 May 2024: pmult q b) r) r' =? pminus (?padd (?pmult q b') r') r'" using ldiv and that unfolding long_divides_def by auto hence eq: "?padd (?pmult q (?pminus b b')) (?pminus ... r r')R" using in_carrier by algebra have "b = b'" proof (assume "b b'" hence pminus:

23 Feb 2024: 11),14878-14891.</p> <p><i>Heritability of Haemodynamics in the Ascending Aorta</i>.McGurk KA, Owen B,<b>Watson WD</b>, Nethonoda RM, Cordell HJ, Farrall M, Rider OJ, Watkins ... JJ, Sayeed RA, Petrou M, Krasopoulos G, Lake HA, Raman B,<b>Watson WD</b>,

23 May 2024: syntax begin lemma transfer_rule_numeral: ‹(R)› if [transfer_rule]: ‹R› ‹R› ‹(R ===> R ===> R)› for R :: ‹'a::{b::{› proof - have "(R) (λk. ... b)k) 0)› using numeral_add_unfold_funpow [where? 'a = 'b, of _ 0] by (simp add:

23 May 2024: A B = (A-B) B" by auto then have "emeasure M (A B)M (A-B)M B" by (ultimately show? ... AE x in M. R x A B) F (AE x in M.

23 May 2024: a A b B}" definition refl' :: "('a 'a)where "refl' r x. ... set xs = Axs))inductive fold_graph' :: "('a 'b 'b) 'b 'a set 'b bool" where "fold_graph' f z {} z" | "⟦x A; fold_graph' f z (A - {x}) y⟧ fold_graph'

23 May 2024: a} Ba,B)" by blast lemma cons_commute: "cons(a, cons(b, C))b, cons(a, C))" by blast lemma cons_absorb: "a: B cons(a,B) = B" by blast lemma ... A(i)) = (iI. {i} A(i))" by blast lemma times_subset_iff: "(A'B' AB) (A'B'A'A) (B'B))" by blast lemma

23 May 2024: based on Lawrence Paulson's book Logic and Computation.› subsection ‹Natural Deduction Rules for LCF› class cpo = "term" default_sort cpo typedecl tr typedecl void typedecl ('a,'b) prod (infixl "" 6) ... typedecl ('a,'b) sum (infixl "" 5) instance

23 May 2024: i d x if (span B) dproof - have B: "card BB" using dim_unique[of B B "card B"]of B] by auto have "dim Ba set)" using ... L = Lb" usingof "B"] affine_affine_hull[of B] B by auto then have "dim LLb" by auto moreover have "card BLb" and "finite B" usingby

23 May 2024: a' s a a'" assumes b: "b t" "b'. b' t b b'" assumes eq: "s - {a} = t - {b}" shows "s = t" proof cases assume "nwithshow? ... a' s a' a" assumes b: "b t" "b'. b' t b' b" assumes eq: "s - {a} = t - {b}" shows "s = t" proof (cases n) assume "nwithshow?

23 Feb 2024: D, Lopez A, Saez B, Taylor-King JP, Prosper F, Fortelny Nsup#/sup, Huntly BJPsup#/sup. ... to other functional changes associated with ageing.”/p pbSearching for cellular changes/b/p pAll human cells acquire genetic changes throughout life, known as

23 May 2024: a'b'b" assume "module_on S s" then interpret module_on S s. ... on S2 s2 for S1 :: "'b::and S2 :: "'c::and s1 :: "'a::comm_ring_1 'b 'b" (infixr "a" 75) and s2 :: "'a::comm_ring_1 'c 'c" (infixr "b" 75)