Search

23 May 2024: rArB" usingby blast have "(A < B)B A)" usingof r A B] by blast also have "…r Br A)" usingby blast also have "…r Ar B)" usingby blast finally show? ... 1 have "(a',a')r f (b',b')r f" unfolding dir_image_def by auto } thus?

23 May 2024: inner a x < b}" unfolding convex_def by (auto simp:lemma convex_halfspace_gt: "convex {x. ... b}" and "a<.b}" and "a.<b}" and "a<.<b}" proof - have "{ax.

23 Feb 2024: L, Barcenas-Morales G, Pollock DD, Goldstein RA, Smielewska A, Skittrall JP, Gouliouris T, Goodfellow IG, Gkrania-Klotsas E, Illingworth C, McCoy LE,<span ... WDF,</span><span>Hill</span><span>A,</span><b>Gupta</b><b>RK</b><span>.</span><span>Reduced

4 Jun 2024: 225x300.jpeg 225w" sizes="(max-width: 240px) 100vw, 240px" //div divb/b/div pbPoetry reading: Anne Portugal/b/p pbFebruary 18th 17.00–18.00 /b/p pbJudith E. ... Wilson Drama Studio, Faculty of English, /b/p pb9 West Road, Cambridge CB3 9DP/bb/b/p pThe

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: B x) a A b B a" by auto lemma INT_E [elim]: "b (xA. ... A B))" "AA else (B. B A))" by auto lemma Un_Union_image: "(xC.

23 Feb 2024: Kew, K. Jestice, strongM. R. Wills/strong, and M. B. Reeves. strong2012/strong. ... Derhovanessian, T. Fulop, P. Griffiths, B. Grubeck-Loebenstein, K. Hamprecht, G. Jahn, F.

23 May 2024: and "a b" "b a" shows "P" using assms by (elimlemma (in weak_partial_order) lless_trans [trans]: assumes "a b" "b c" and carr[simp]: "aL" "bL" "cL" shows "a ... add:subsubsection ‹Idempotent functions› definition idempotent :: "('a, 'b) gorder_scheme

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="" ... ogab="" data-ogsc="" data-ogsb=""translation/spanworkshop/i/b/div

23 May 2024: simp 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 Feb 2024: antibody-response" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">antibody response</a></div><div class="field-item odd"><a href="/subject/b-cells" typeof="skos:Concept" property="rdfs:label ... WDF,</span><span>Hill</span><span>A,

23 Feb 2024: Saeb-Parsy K<b></b>, Markaki AE , Vallier E, Sampaziotis F (2019). ... MR, Fitzgerald RC, Handford PA, Campbell PJ<b>, </b>Saeb-Parsy K, Jones PH (2018).

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: f aa" definition zero_l_neutral :: "('a::zero 'b 'b) bool" where "zero_l_neutral f == a. ... fmul fadd A B" by simp qed definition r_distributive :: "('a 'b 'b) ('b 'b 'b) bool" where "r_distributive fmul fadd == a u v.

23 May 2024: mk_disjoint_insert by fastforce lemma fst_Pi: "A B A" and snd_Pi: "A B B" by auto subsection ‹Composition With a Restricted Domain: <term>‹compose›› lemma funcset_compose: "f ... E. x{a}. B x) = (b B a. {λx {a}. b})" apply (auto simp: PiE_iff

23 May 2024: transfer by simp lift_definition ffold :: "('a 'b 'b) 'b 'a fset 'b" is Finite_Set.fold. ... A || C" by (lemma fsubset_pfsubset_trans: "A || B B || C A || C" by (lemma pfsubset_imp_ex_fmem: "A || B b.

23 May 2024: thesis by simp qed lemma permutes_bij_inv_into: ‹contributor ‹Lukas Bulwahn›› fixes A :: "'a set" and B :: "'b set" assumes "p permutes A" and "bij_betw f A B" shows "( ... f) B A" by (auto simp add:then have "bij_betw (f pA f) B B" by (simp add:

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 May 2024: iso_tuple_fst_update :: "('a, 'b, 'c) tuple_isomorphism ('b 'b) ('a 'a)" where "iso_tuple_fst_update isom fisomfisom" definition iso_tuple_snd_update :: "('a, 'b, 'c) tuple_isomorphism ('c ... b 'b) ('a 'a)) ('a 'b) bool" where

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: P a b; P b c; a b; b c⟧ P a c" assumes 3: "x. ... N = (d, t, e) d < b b e" by auto obtain d t e where D_eq: "D!

23 May 2024: T (Rep b) b) R = TT" unfoldingby auto lemma Quotient_alt_def5: "Quotient R Abs Rep T TAbsRep TR = T OO T" unfoldingby blast lemma fun_quotient: assumes 1: "Quotient R1 ... correspondence relation› definition POS :: "('a 'b bool) ('a 'bwhere "POS A B A B

23 May 2024: A B" "B C" and measure: "emeasure M AM C" "emeasure M Ashows "BM" proof - have "B - AM" proof (show "B - A C - A" using subset by auto show "C - AM" ... A - B)M" using A by blast also have "A (B - A) - (A - B) = B" by auto finally show "BM".

23 May 2024: a, 's2)where "fair_implements C ACACACA" lemma implements_trans: "A =<| B B =<| C A =<| C" by (auto simp add: ioa_implements_def) subsection ‹Modules› subsubsection ‹Execution, schedule and trace modules› ... mk_trace›› (alternative

23 May 2024: S::'a :: {b (b'<b. ... xS. b' < x) Sup S = b" by (simp: not_le[symmetric] setle_def) lemma cInf_unique: "b <= (S::'a :: {b'>b.

23 May 2024: xBB x bmx" proof fix x assume x: "xB" have "busing ‹independent B› ‹b B› dependent_zero by blast have [simp]: "b b'b' = bb)if "b B" "b' B" for ... lemma continuous_on_representation: fixes B :: "'N::assumes "finite B" "independent B" "b B" "B"

23 Feb 2024: J. Biol. Chem. 276, 15059–15065 (2001).</li> </ul> <p><b></b></p> <p><b></b></p> </div></div></div><div class="field field-name-field-sd-websites

23 May 2024: bool: "C) = C(C(1)" by (unfoldIntroduction rules for the injections ) lemma InlI [intro!,simp,TC]: "a A Inl(a) AB" by (unfoldlemma InrI [intro!,simp,TC]: "b B Inr(b) ... b): AB b B" by blast lemma sum_iff: "u ABx.

23 May 2024: nm#k))" by (auto intro: less_imp_succ_add) lemma add_lt_elim2: "⟦a # d = b # c; a < b; bcd⟧ c < d" by (drulelemma add_le_elim2: "⟦a # d = b # c; ... add:lemma raw_nat_diff_split: "⟦ab⟧ (P(a #- b)) ((a < b P(dnat.

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

4 Jun 2024: 225x300.jpeg 225w" sizes="(max-width: 240px) 100vw, 240px" //div divb/b/div pbPoetry reading: Anne Portugal/b/p pbFebruary 18th 17.00–18.00 /b/p pbJudith E. ... Wilson Drama Studio, Faculty of English, /b/p pb9 West Road, Cambridge CB3 9DP/bb/b/p pThe

23 May 2024: a H b H a G⦇carrier := H⦈ b = a b" using assms by simp have "a b. ... f = h and? A = "carrier G"] by auto have aux_lemma: "a b. ⟦

23 May 2024: k K open k" unfolding eq by auto from ex_countable_basis obtain B :: "'awhere B: "b. ... fix X::"'a set" assume "open X" from open_countable_basisE[OF this] obtain B' where B': "B' B" "XB'".

23 May 2024: are for backward compatibility.› lemma irreflp_on_irrefl_on_eq [A (λa b. ... f x, f y) r}" definition inv_imagep :: "('b 'b bool) ('a 'b) 'a 'a bool" where "inv_imagep r f = (λx y.

23 May 2024: 𝟬)" by (induction n) (auto) lemma scalar_coeff: "aRλb. a b) p) = (λi. ... a_p2 = "(map (λb. a b) p2)a # p1)) 𝟬)" have "a # p1))λ_.

23 May 2024: a a') x b b'}" usingby (force simp: inner_left_distrib) have "S {x. ... b)b" and "a b" and u01: "u" "uusing assms by (auto simp:then have "(u).

23 May 2024: y,x⟩: r y B) x B A<=B›› lemma wf_onI2: assumes prem: "y B. ... well-founded induction then we have <term>‹wf(r)›.› lemma wfI: "⟦field(r)<=A; y B.

23 May 2024: a 'bwhere "Inr_Rep b x y p y = bp" definition "sum = {f. ... A <> BAB" hide_const (open) Plus ― ‹Valuable identifier› lemma InlI [intro!]: "a A Inl a A <> B" by (simp add: Plus_def) lemma InrI [intro!]: "b B Inr b A <> B"

23 May 2024: x A" | A B where "x D" "A face_of B" "B " "B 𝒢" "aff_dim AT" "x A" using x by (auto simp: _def) then have xrel: "xD" proof cases ... b" using bounded_subset_cbox_symmetric by blast define bbox where "bboxbbhave "b) b bbox" by (auto simp:intro!:

23 May 2024: subsection ‹Simple types› schematic_goal "A: AA :? T" by (schematic_goal "A: λa:A. a :? T" by (schematic_goal "A: B: b:B λx:A. ... B :? T" by (schematic_goal (in Lomega) "B: b:B (λy:B.

23 May 2024: a A}" definition "Grp A f = (λa b. b = f a a A)" definition vimage2p where "vimage2p f g R = (λx y. ... y, x)) AR)" by auto lemma predicate2_eqD: "A = B A a b B a b" by simp lemma case_sum_o_inj: "case_sum f gf" "case_sum f gg"

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: h xa.b} g (h x) = x" assumes range: "{a.bh" shows "f) lborel h) {a.bλx. ... where B=B])(auto simp add: f_bounded) then show "enn2real (. - f x M') = x. f x M'" by(simp add: real_lebesgue_integral_def) qed qed simp_all finally show?

23 May 2024: f b b}" by auto interpret bijection f by‹bij f›) from fin show "f)a. ... f b b}" then have "bij f" by simp interpret bijection f by‹bij f›) show "{a.

23 May 2024: a - b)x = a (ax2 b) a x b b x" by (simp add:have "(kn. ... norm(f x - g x) < e)" proof - { fix b :: 'b assume "bhave "pp (x S.

23 May 2024: thesis by simp qed lemma norm_minus_commute: "norm (a - b)b - a)" proof - have "b - a))b - a)" by (then show? ... norm aba - b)" proof - have "norm (a - b b)a - b)b" by (then show?

23 May 2024: eval B y)" by simp show? thesis proof (cases "ABcase True then obtain a b where a: "eval A a" and b: "eval B b" by (blast elim: not_bot) withhave " ... holds_if_pred: "b) = b" unfoldingby (cases b) (auto intro: singleI elim: botE) lemma if_pred_holds: "P)

23 May 2024: b B (b,a) r)⟧ (supr B, a) r" by(auto simp add:lemma equals_supr_Above: assumes "a Above B" " a'. ... b. b B a b (b,a) r" and MINIM: " a'. ⟦a'r; b.

23 Feb 2024: The overwhelming majority of Wnt research to date has focussed on the canonical Wnt/b-catenin pathway, given its early identification as a driver of cancer. ... b>) 2016</span></span></span></p> <p><span><span><span>Nixon-Abell J, Berwick DC, Granno S,

23 Feb 2024: Before his postdoctoral work in Cambridge, Sam completed his B.Sc. in Biological Sciences at the University of Guelph and a Ph.D. ... Salama1 ,<b>Tammy Dougan1</b>, Jeremy B.Levy1, Terry Cook2 , Steve Morgan3, Sarah Naudeer4, Andrew J.