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author | berghofe |

Wed, 07 May 2008 10:59:23 +0200 | |

changeset 26813 | 6a4d5ca6d2e5 |

parent 26812 | c0fa62fa0e5b |

child 26814 | b3e8d5ec721d |

Rephrased calculational proofs to avoid problems with HO unification

src/HOL/Isar_examples/MutilatedCheckerboard.thy | file | annotate | diff | comparison | revisions | |

src/HOL/ex/CTL.thy | file | annotate | diff | comparison | revisions |

--- a/src/HOL/Isar_examples/MutilatedCheckerboard.thy Wed May 07 10:59:22 2008 +0200 +++ b/src/HOL/Isar_examples/MutilatedCheckerboard.thy Wed May 07 10:59:23 2008 +0200 @@ -134,7 +134,7 @@ let ?a = "{i} <*> {2 * n + 1} Un {i} <*> {2 * n}" have "?B (Suc n) = ?a Un ?B n" by (auto simp add: Sigma_Suc Un_assoc) - also have "... : ?T" + moreover have "... : ?T" proof (rule tiling.Un) have "{(i, 2 * n), (i, 2 * n + 1)} : domino" by (rule domino.horiz) @@ -143,7 +143,7 @@ show "?B n : ?T" by (rule Suc) show "?a <= - ?B n" by blast qed - finally show ?case . + ultimately show ?case by simp qed lemma dominoes_tile_matrix: @@ -156,13 +156,13 @@ case (Suc m) let ?t = "{m} <*> below (2 * n)" have "?B (Suc m) = ?t Un ?B m" by (simp add: Sigma_Suc) - also have "... : ?T" + moreover have "... : ?T" proof (rule tiling_Un) show "?t : ?T" by (rule dominoes_tile_row) show "?B m : ?T" by (rule Suc) show "?t Int ?B m = {}" by blast qed - finally show ?case . + ultimately show ?case by simp qed lemma domino_singleton: @@ -224,8 +224,8 @@ have "EX i j. ?e a b = {(i, j)}" by (rule domino_singleton) then show ?thesis by (blast intro: that) qed - also have "... Un ?e t b = insert (i, j) (?e t b)" by simp - also have "card ... = Suc (card (?e t b))" + moreover have "... Un ?e t b = insert (i, j) (?e t b)" by simp + moreover have "card ... = Suc (card (?e t b))" proof (rule card_insert_disjoint) from `t \<in> tiling domino` have "finite t" by (rule tiling_domino_finite) @@ -234,7 +234,7 @@ from e have "(i, j) : ?e a b" by simp with at show "(i, j) ~: ?e t b" by (blast dest: evnoddD) qed - finally show "?thesis b" . + ultimately show "?thesis b" by simp qed then have "card (?e (a Un t) 0) = Suc (card (?e t 0))" by simp also from hyp have "card (?e t 0) = card (?e t 1)" .

--- a/src/HOL/ex/CTL.thy Wed May 07 10:59:22 2008 +0200 +++ b/src/HOL/ex/CTL.thy Wed May 07 10:59:23 2008 +0200 @@ -95,7 +95,7 @@ proof assume "x \<in> gfp (\<lambda>s. - f (- s))" then obtain u where "x \<in> u" and "u \<subseteq> - f (- u)" - by (auto simp add: gfp_def Sup_set_def) + by (auto simp add: gfp_def Sup_set_eq) then have "f (- u) \<subseteq> - u" by auto then have "lfp f \<subseteq> - u" by (rule lfp_lowerbound) from l and this have "x \<notin> u" by auto @@ -253,8 +253,8 @@ proof - { have "\<AG> (p \<rightarrow> \<AX> p) \<subseteq> p \<rightarrow> \<AX> p" by (rule AG_fp_1) - also have "p \<inter> p \<rightarrow> \<AX> p \<subseteq> \<AX> p" .. - finally have "?lhs \<subseteq> \<AX> p" by auto + moreover have "p \<inter> p \<rightarrow> \<AX> p \<subseteq> \<AX> p" .. + ultimately have "?lhs \<subseteq> \<AX> p" by auto } moreover { @@ -262,7 +262,8 @@ also have "\<dots> \<subseteq> \<AX> \<dots>" by (rule AG_fp_2) finally have "?lhs \<subseteq> \<AX> \<AG> (p \<rightarrow> \<AX> p)" . } - ultimately have "?lhs \<subseteq> \<AX> p \<inter> \<AX> \<AG> (p \<rightarrow> \<AX> p)" .. + ultimately have "?lhs \<subseteq> \<AX> p \<inter> \<AX> \<AG> (p \<rightarrow> \<AX> p)" + by (rule Int_greatest) also have "\<dots> = \<AX> ?lhs" by (simp only: AX_int) finally show ?thesis . qed