# HG changeset patch # User wenzelm # Date 1675279293 -3600 # Node ID 816959264c326d3c9c000683196cadb61776cb62 # Parent e0e9f1b4c844c358c5e922defd09220d1ca3b1e3 isabelle update -u cite -l ""; diff -r e0e9f1b4c844 -r 816959264c32 src/HOL/BNF_Cardinal_Order_Relation.thy --- a/src/HOL/BNF_Cardinal_Order_Relation.thy Wed Feb 01 20:07:13 2023 +0100 +++ b/src/HOL/BNF_Cardinal_Order_Relation.thy Wed Feb 01 20:21:33 2023 +0100 @@ -759,7 +759,7 @@ theorem \Card_order_Times_same_infinite\, which states that self-product does not increase cardinality -- the proof of this fact adapts a standard set-theoretic argument, as presented, e.g., in the proof of theorem 1.5.11 -at page 47 in @{cite "card-book"}. Then everything else follows fairly easily.\ +at page 47 in \<^cite>\"card-book"\. Then everything else follows fairly easily.\ lemma infinite_iff_card_of_nat: "\ finite A \ ( |UNIV::nat set| \o |A| )" diff -r e0e9f1b4c844 -r 816959264c32 src/HOL/Binomial.thy --- a/src/HOL/Binomial.thy Wed Feb 01 20:07:13 2023 +0100 +++ b/src/HOL/Binomial.thy Wed Feb 01 20:21:33 2023 +0100 @@ -718,7 +718,7 @@ using binomial_symmetric[of k n] by (simp add: binomial_gbinomial [symmetric]) -text \The absorption identity (equation 5.5 @{cite \p.~157\ GKP_CM}): +text \The absorption identity (equation 5.5 \<^cite>\\p.~157\ in GKP_CM\): \[ {r \choose k} = \frac{r}{k}{r - 1 \choose k - 1},\quad \textnormal{integer } k \neq 0. \]\ @@ -728,7 +728,7 @@ text \The absorption identity is written in the following form to avoid division by $k$ (the lower index) and therefore remove the $k \neq 0$ -restriction @{cite \p.~157\ GKP_CM}: +restriction \<^cite>\\p.~157\ in GKP_CM\: \[ k{r \choose k} = r{r - 1 \choose k - 1}, \quad \textnormal{integer } k. \]\ @@ -740,7 +740,7 @@ by (cases n) (simp_all add: binomial_eq_0 Suc_times_binomial del: binomial_Suc_Suc mult_Suc) text \The absorption companion identity for natural number coefficients, - following the proof by GKP @{cite \p.~157\ GKP_CM}:\ + following the proof by GKP \<^cite>\\p.~157\ in GKP_CM\:\ lemma binomial_absorb_comp: "(n - k) * (n choose k) = n * ((n - 1) choose k)" (is "?lhs = ?rhs") proof (cases "n \ k") @@ -771,7 +771,7 @@ by (subst choose_reduce_nat) simp_all text \ - Equation 5.9 of the reference material @{cite \p.~159\ GKP_CM} is a useful + Equation 5.9 of the reference material \<^cite>\\p.~159\ in GKP_CM\ is a useful summation formula, operating on both indices: \[ \sum\limits_{k \leq n}{r + k \choose k} = {r + n + 1 \choose n}, @@ -793,7 +793,7 @@ subsubsection \Summation on the upper index\ text \ - Another summation formula is equation 5.10 of the reference material @{cite \p.~160\ GKP_CM}, + Another summation formula is equation 5.10 of the reference material \<^cite>\\p.~160\ in GKP_CM\, aptly named \emph{summation on the upper index}:\[\sum_{0 \leq k \leq n} {k \choose m} = {n + 1 \choose m + 1}, \quad \textnormal{integers } m, n \geq 0.\] \ diff -r e0e9f1b4c844 -r 816959264c32 src/HOL/GCD.thy --- a/src/HOL/GCD.thy Wed Feb 01 20:07:13 2023 +0100 +++ b/src/HOL/GCD.thy Wed Feb 01 20:21:33 2023 +0100 @@ -2011,7 +2011,7 @@ lemma gcd_mult_distrib_nat: "k * gcd m n = gcd (k * m) (k * n)" for k m n :: nat - \ \@{cite \page 27\ davenport92}\ + \ \\<^cite>\\page 27\ in davenport92\\ by (simp add: gcd_mult_left) lemma gcd_mult_distrib_int: "\k\ * gcd m n = gcd (k * m) (k * n)" diff -r e0e9f1b4c844 -r 816959264c32 src/HOL/HOL.thy --- a/src/HOL/HOL.thy Wed Feb 01 20:07:13 2023 +0100 +++ b/src/HOL/HOL.thy Wed Feb 01 20:21:33 2023 +0100 @@ -57,7 +57,7 @@ subsection \Primitive logic\ text \ -The definition of the logic is based on Mike Gordon's technical report @{cite "Gordon-TR68"} that +The definition of the logic is based on Mike Gordon's technical report \<^cite>\"Gordon-TR68"\ that describes the first implementation of HOL. However, there are a number of differences. In particular, we start with the definite description operator and introduce Hilbert's \\\ operator only much later. Moreover, axiom \(P \ Q) \ (Q \ P) \ (P = Q)\ is derived from the other diff -r e0e9f1b4c844 -r 816959264c32 src/HOL/Wellfounded.thy --- a/src/HOL/Wellfounded.thy Wed Feb 01 20:07:13 2023 +0100 +++ b/src/HOL/Wellfounded.thy Wed Feb 01 20:21:33 2023 +0100 @@ -617,7 +617,7 @@ text \ Inductive definition of the accessible part \acc r\ of a - relation; see also @{cite "paulin-tlca"}. + relation; see also \<^cite>\"paulin-tlca"\. \ inductive_set acc :: "('a \ 'a) set \ 'a set" for r :: "('a \ 'a) set"