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methylene revised this gist
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -9,7 +9,8 @@ http://en.wikipedia.org/wiki/Peirce_law Definition peirce := forall (p q : Prop), ((p -> q) -> p) -> p. Definition lem := forall p : Prop, p\/ ~ p. Theorem peirce_implies_lem: peirce -> lem. @@ -48,4 +49,4 @@ Proof. intro. intro. (* How to finish proof of w1_implies_lem? *) -
methylene revised this gist
Jan 17, 2013 . 1 changed file with 2 additions and 2 deletions.There are no files selected for viewing
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -41,11 +41,11 @@ Qed. (* How to prove w0_implies_w1 without 'firstorder magic'? *) Lemma w1_implies_lem: w1 -> lem. Proof. unfold w1, lem. intro. intro. (* How to prove w1_implies_lem? *) -
methylene revised this gist
Jan 16, 2013 . 1 changed file with 2 additions and 2 deletions.There are no files selected for viewing
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -31,14 +31,14 @@ Definition w1 := forall (p : Prop), (p \/ ~ p -> ~ (p \/ ~ p)) -> p \/ ~ p. Lemma w0_implies_w1: w0 -> w1. Proof. unfold w0, w1. firstorder. Qed. (* How to prove w0_implies_w1 without 'firstorder magic'? *) Lemma lem_from_w1: w1 -> lem. -
methylene created this gist
Jan 16, 2013 .There are no files selected for viewing
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,51 @@ (* https://www.youtube.com/watch?v=7sk8hPWAMSw http://en.wikipedia.org/wiki/Law_of_excluded_middle http://en.wikipedia.org/wiki/Peirce_law *) Definition peirce := forall (p q : Prop), ((p -> q) -> p) -> p. Definition lem := forall p, p\/ ~ p. Theorem peirce_implies_lem: peirce -> lem. Proof. unfold peirce, lem. intros. apply H with (q := ~ (p \/ ~ p)). firstorder. Qed. (* Not so fast please. Can we break the last two steps down a bit? *) Definition w0 := forall (p : Prop), ((p -> ~ (p \/ ~ p) ) -> p) -> p. Definition w1 := forall (p : Prop), (p \/ ~ p -> ~ (p \/ ~ p)) -> p \/ ~ p. Lemma w1_from_w0: w0 -> w1. Proof. unfold w0, w1. firstorder. Qed. (* How to prove w1_from_w0 without 'firstorder magic'? *) Lemma lem_from_w1: w1 -> lem. Proof. unfold w1, lem. intro. intro. (* How do I prove theorem? *)