# HG changeset patch # User wenzelm # Date 1205868811 -3600 # Node ID 9e9e67e33557251703df13f4f3aecdc460a0b188 # Parent cb3badaa192eaeaba1f7e4cef4ece7159dee0a18 removed redundant less_trans, less_linear, le_imp_less_or_eq, le_less_trans, less_le_trans (cf. Orderings.thy); diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/HoareParallel/Gar_Coll.thy --- a/src/HOL/HoareParallel/Gar_Coll.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/HoareParallel/Gar_Coll.thy Tue Mar 18 20:33:31 2008 +0100 @@ -185,7 +185,7 @@ apply (erule_tac x=i in allE , erule (1) notE impE) apply simp apply clarify - apply (drule Nat.le_imp_less_or_eq) + apply (drule_tac y = r in le_imp_less_or_eq) apply (erule disjE) apply (subgoal_tac "Suc (ind x)\r") apply fast @@ -276,7 +276,7 @@ apply (erule_tac x=i in allE , erule (1) notE impE) apply simp apply clarify - apply (drule Nat.le_imp_less_or_eq) + apply (drule_tac y = r in le_imp_less_or_eq) apply (erule disjE) apply (subgoal_tac "Suc (ind x)\r") apply fast @@ -309,7 +309,7 @@ apply (erule_tac x=i in allE , erule (1) notE impE) apply simp apply clarify - apply (drule Nat.le_imp_less_or_eq) + apply (drule_tac y = r in le_imp_less_or_eq) apply (erule disjE) apply (subgoal_tac "Suc (ind x)\r") apply fast diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/HoareParallel/Graph.thy --- a/src/HOL/HoareParallel/Graph.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/HoareParallel/Graph.thy Tue Mar 18 20:33:31 2008 +0100 @@ -336,7 +336,7 @@ apply(erule_tac P = "\i. i < Suc nat \ ?P i" and x = "nat" in allE) apply simp apply(case_tac "j\R") - apply(drule Nat.le_imp_less_or_eq) + apply(drule le_imp_less_or_eq [of _ R]) apply(erule disjE) apply(erule allE , erule (1) notE impE) apply force diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/HoareParallel/Mul_Gar_Coll.thy --- a/src/HOL/HoareParallel/Mul_Gar_Coll.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/HoareParallel/Mul_Gar_Coll.thy Tue Mar 18 20:33:31 2008 +0100 @@ -383,7 +383,7 @@ apply force --{* 1 subgoal left *} apply clarify -apply(drule Nat.le_imp_less_or_eq) +apply(drule_tac x = "ind x" in le_imp_less_or_eq) apply (simp_all add:Blacks_def) done diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/Hyperreal/Integration.thy --- a/src/HOL/Hyperreal/Integration.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/Hyperreal/Integration.thy Tue Mar 18 20:33:31 2008 +0100 @@ -561,7 +561,7 @@ apply (frule partition_eq_bound) apply (drule_tac [2] partition_gt, auto) apply (metis dense_linear_order_class.dlo_simps(8) not_less partition_rhs partition_rhs2) -apply (metis Nat.le_less_trans dense_linear_order_class.dlo_simps(8) nat_le_linear partition_eq_bound partition_rhs2) +apply (metis le_less_trans dense_linear_order_class.dlo_simps(8) nat_le_linear partition_eq_bound partition_rhs2) done lemma lemma_additivity4_psize_eq: @@ -574,7 +574,7 @@ apply (auto intro: partition_lt_Suc) apply (drule_tac n = n in partition_lt_gen, assumption) apply (arith, arith) -apply (cut_tac m = na and n = "psize D" in Nat.less_linear) +apply (cut_tac x = na and y = "psize D" in less_linear) apply (auto dest: partition_lt_cancel) apply (rule_tac x=N and y=n in linorder_cases) apply (drule_tac x = n and P="%m. N \ m --> ?f m = ?g m" in spec, simp) diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/Hyperreal/Poly.thy --- a/src/HOL/Hyperreal/Poly.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/Hyperreal/Poly.thy Tue Mar 18 20:33:31 2008 +0100 @@ -739,7 +739,7 @@ ==> EX! n. ([-a, 1] %^ n) divides p & ~(([-a, 1] %^ (Suc n)) divides p)" apply (auto intro: poly_order_exists simp add: less_linear simp del: pmult_Cons pexp_Suc) -apply (metis Suc_leI Nat.less_linear poly_exp_divides) +apply (metis Suc_leI less_linear poly_exp_divides) done text{*Order*} diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/Library/Permutation.thy --- a/src/HOL/Library/Permutation.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/Library/Permutation.thy Tue Mar 18 20:33:31 2008 +0100 @@ -188,7 +188,7 @@ apply (subgoal_tac "set (a#list) = set (ysa@a#zs) & distinct (a#list) & distinct (ysa@a#zs)") apply (fastsimp simp add: insert_ident) apply (metis distinct_remdups set_remdups) - apply (metis Nat.le_less_trans Suc_length_conv length_remdups_leq less_Suc_eq nat_less_le) + apply (metis le_less_trans Suc_length_conv length_remdups_leq less_Suc_eq nat_less_le) done lemma perm_remdups_iff_eq_set: "remdups x <~~> remdups y = (set x = set y)" diff -r cb3badaa192e -r 9e9e67e33557 src/HOL/NumberTheory/Factorization.thy --- a/src/HOL/NumberTheory/Factorization.thy Tue Mar 18 20:33:29 2008 +0100 +++ b/src/HOL/NumberTheory/Factorization.thy Tue Mar 18 20:33:31 2008 +0100 @@ -295,7 +295,7 @@ lemma primel_prod_less: "primel (x # xs) ==> primel ys ==> prod (x # xs) = prod ys ==> prod xs < prod ys" - by (metis Nat.less_asym linorder_neqE_nat mult_less_cancel2 nat_0_less_mult_iff + by (metis less_asym linorder_neqE_nat mult_less_cancel2 nat_0_less_mult_iff nat_less_le nat_mult_1 prime_def primel_hd_tl primel_prod_gz prod.simps(2)) lemma prod_one_empty: