src/HOL/Library/Zorn.thy
 changeset 44890 22f665a2e91c parent 35175 61255c81da01 child 46008 c296c75f4cf4
```     1.1 --- a/src/HOL/Library/Zorn.thy	Sun Sep 11 22:56:05 2011 +0200
1.2 +++ b/src/HOL/Library/Zorn.thy	Mon Sep 12 07:55:43 2011 +0200
1.3 @@ -480,12 +480,12 @@
1.4          by(auto simp add:wf_eq_minimal Field_def Domain_def Range_def) metis
1.5        thus ?thesis using `wf(m-Id)` `x \<notin> Field m`
1.6          wf_subset[OF `wf ?s` Diff_subset]
1.7 -        by (fastsimp intro!: wf_Un simp add: Un_Diff Field_def)
1.8 +        by (fastforce intro!: wf_Un simp add: Un_Diff Field_def)
1.9      qed
1.10      ultimately have "Well_order ?m" by(simp add:order_on_defs)
1.11  --{*We show that the extension is above m*}
1.12      moreover hence "(m,?m) : I" using `Well_order m` `x \<notin> Field m`
1.13 -      by(fastsimp simp:I_def init_seg_of_def Field_def Domain_def Range_def)
1.14 +      by(fastforce simp:I_def init_seg_of_def Field_def Domain_def Range_def)
1.15      ultimately
1.16  --{*This contradicts maximality of m:*}
1.17      have False using max `x \<notin> Field m` unfolding Field_def by blast
1.18 @@ -501,7 +501,7 @@
1.19      using well_ordering[where 'a = "'a"] by blast
1.20    let ?r = "{(x,y). x:A & y:A & (x,y):r}"
1.21    have 1: "Field ?r = A" using wo univ
1.22 -    by(fastsimp simp: Field_def Domain_def Range_def order_on_defs refl_on_def)
1.23 +    by(fastforce simp: Field_def Domain_def Range_def order_on_defs refl_on_def)
1.24    have "Refl r" "trans r" "antisym r" "Total r" "wf(r-Id)"
1.25      using `Well_order r` by(simp_all add:order_on_defs)
1.26    have "Refl ?r" using `Refl r` by(auto simp:refl_on_def 1 univ)
```