# HG changeset patch # User bulwahn # Date 1327742566 -3600 # Node ID a49c89df7c924f1299b91448bdb5ae0f5980dc78 # Parent b159ca4e268bda94c9e3584cbd14fc99ec84d0a2 moving declarations back to the section they seem to belong to (cf. afffe1f72143) diff -r b159ca4e268b -r a49c89df7c92 src/HOL/Nat.thy --- a/src/HOL/Nat.thy Sat Jan 28 06:13:03 2012 +0100 +++ b/src/HOL/Nat.thy Sat Jan 28 10:22:46 2012 +0100 @@ -1616,6 +1616,17 @@ lemma Suc_diff_Suc: "n < m \ Suc (m - Suc n) = m - n" by simp +(*The others are + i - j - k = i - (j + k), + k \ j ==> j - k + i = j + i - k, + k \ j ==> i + (j - k) = i + j - k *) +lemmas add_diff_assoc = diff_add_assoc [symmetric] +lemmas add_diff_assoc2 = diff_add_assoc2[symmetric] +declare diff_diff_left [simp] add_diff_assoc [simp] add_diff_assoc2[simp] + +text{*At present we prove no analogue of @{text not_less_Least} or @{text +Least_Suc}, since there appears to be no need.*} + text{*Lemmas for ex/Factorization*} lemma one_less_mult: "[| Suc 0 < n; Suc 0 < m |] ==> Suc 0 < m*n" @@ -1669,17 +1680,6 @@ lemma zero_induct: "P k ==> (!!n. P (Suc n) ==> P n) ==> P 0" using inc_induct[of 0 k P] by blast -(*The others are - i - j - k = i - (j + k), - k \ j ==> j - k + i = j + i - k, - k \ j ==> i + (j - k) = i + j - k *) -lemmas add_diff_assoc = diff_add_assoc [symmetric] -lemmas add_diff_assoc2 = diff_add_assoc2[symmetric] -declare diff_diff_left [simp] add_diff_assoc [simp] add_diff_assoc2[simp] - -text{*At present we prove no analogue of @{text not_less_Least} or @{text -Least_Suc}, since there appears to be no need.*} - subsection {* The divides relation on @{typ nat} *}