# HG changeset patch # User wenzelm # Date 1211123003 -7200 # Node ID ed3a58a9eae132b71f8dc7ec15fc6b73473c36c4 # Parent e3f04fdd994d358929cd24db212bf26c58a02998 converted to regular application syntax; diff -r e3f04fdd994d -r ed3a58a9eae1 src/FOL/ex/First_Order_Logic.thy --- a/src/FOL/ex/First_Order_Logic.thy Sun May 18 17:03:20 2008 +0200 +++ b/src/FOL/ex/First_Order_Logic.thy Sun May 18 17:03:23 2008 +0200 @@ -110,7 +110,7 @@ equal :: "i \ i \ o" (infixl "=" 50) where refl [intro]: "x = x" and - subst: "x = y \ P(x) \ P(y)" + subst: "x = y \ P x \ P y" theorem trans [trans]: "x = y \ y = z \ x = z" by (rule subst) @@ -128,32 +128,32 @@ All :: "(i \ o) \ o" (binder "\" 10) and Ex :: "(i \ o) \ o" (binder "\" 10) where - allI [intro]: "(\x. P(x)) \ \x. P(x)" and - allD [dest]: "\x. P(x) \ P(a)" and - exI [intro]: "P(a) \ \x. P(x)" and - exE [elim]: "\x. P(x) \ (\x. P(x) \ C) \ C" + allI [intro]: "(\x. P x) \ \x. P x" and + allD [dest]: "\x. P x \ P a" and + exI [intro]: "P a \ \x. P x" and + exE [elim]: "\x. P x \ (\x. P x \ C) \ C" -lemma "(\x. P(f(x))) \ (\y. P(y))" +lemma "(\x. P (f x)) \ (\y. P y)" proof - assume "\x. P(f(x))" - then show "\y. P(y)" + assume "\x. P (f x)" + then show "\y. P y" proof - fix x assume "P(f(x))" + fix x assume "P (f x)" then show ?thesis .. qed qed -lemma "(\x. \y. R(x, y)) \ (\y. \x. R(x, y))" +lemma "(\x. \y. R x y) \ (\y. \x. R x y)" proof - assume "\x. \y. R(x, y)" - then show "\y. \x. R(x, y)" + assume "\x. \y. R x y" + then show "\y. \x. R x y" proof - fix x assume a: "\y. R(x, y)" + fix x assume a: "\y. R x y" show ?thesis proof - fix y from a have "R(x, y)" .. - then show "\x. R(x, y)" .. + fix y from a have "R x y" .. + then show "\x. R x y" .. qed qed qed diff -r e3f04fdd994d -r ed3a58a9eae1 src/Pure/Pure.thy --- a/src/Pure/Pure.thy Sun May 18 17:03:20 2008 +0200 +++ b/src/Pure/Pure.thy Sun May 18 17:03:23 2008 +0200 @@ -14,14 +14,14 @@ lemmas meta_impE = meta_mp [elim_format] lemma meta_spec: - assumes "!!x. PROP P(x)" - shows "PROP P(x)" - by (rule `!!x. PROP P(x)`) + assumes "!!x. PROP P x" + shows "PROP P x" + by (rule `!!x. PROP P x`) lemmas meta_allE = meta_spec [elim_format] lemma swap_params: - "(!!x y. PROP P(x, y)) == (!!y x. PROP P(x, y))" .. + "(!!x y. PROP P x y) == (!!y x. PROP P x y)" .. subsection {* Embedded terms *} @@ -39,22 +39,22 @@ lemma all_conjunction: includes meta_conjunction_syntax - shows "(!!x. PROP A(x) && PROP B(x)) == ((!!x. PROP A(x)) && (!!x. PROP B(x)))" + shows "(!!x. PROP A x && PROP B x) == ((!!x. PROP A x) && (!!x. PROP B x))" proof - assume conj: "!!x. PROP A(x) && PROP B(x)" - show "(!!x. PROP A(x)) && (!!x. PROP B(x))" + assume conj: "!!x. PROP A x && PROP B x" + show "(!!x. PROP A x) && (!!x. PROP B x)" proof - fix x - from conj show "PROP A(x)" by (rule conjunctionD1) - from conj show "PROP B(x)" by (rule conjunctionD2) + from conj show "PROP A x" by (rule conjunctionD1) + from conj show "PROP B x" by (rule conjunctionD2) qed next - assume conj: "(!!x. PROP A(x)) && (!!x. PROP B(x))" + assume conj: "(!!x. PROP A x) && (!!x. PROP B x)" fix x - show "PROP A(x) && PROP B(x)" + show "PROP A x && PROP B x" proof - - show "PROP A(x)" by (rule conj [THEN conjunctionD1, rule_format]) - show "PROP B(x)" by (rule conj [THEN conjunctionD2, rule_format]) + show "PROP A x" by (rule conj [THEN conjunctionD1, rule_format]) + show "PROP B x" by (rule conj [THEN conjunctionD2, rule_format]) qed qed