diff -r 7b86df67cc1a -r f947332d5465 src/FOLP/ex/prop.ML --- a/src/FOLP/ex/prop.ML Sat Jun 20 20:35:38 1998 +0200 +++ b/src/FOLP/ex/prop.ML Mon Jun 22 15:09:59 1998 +0200 @@ -11,66 +11,66 @@ writeln"commutative laws of & and | "; -goal thy "?p : P & Q --> Q & P"; +Goal "?p : P & Q --> Q & P"; by tac; result(); -goal thy "?p : P | Q --> Q | P"; +Goal "?p : P | Q --> Q | P"; by tac; result(); writeln"associative laws of & and | "; -goal thy "?p : (P & Q) & R --> P & (Q & R)"; +Goal "?p : (P & Q) & R --> P & (Q & R)"; by tac; result(); -goal thy "?p : (P | Q) | R --> P | (Q | R)"; +Goal "?p : (P | Q) | R --> P | (Q | R)"; by tac; result(); writeln"distributive laws of & and | "; -goal thy "?p : (P & Q) | R --> (P | R) & (Q | R)"; +Goal "?p : (P & Q) | R --> (P | R) & (Q | R)"; by tac; result(); -goal thy "?p : (P | R) & (Q | R) --> (P & Q) | R"; +Goal "?p : (P | R) & (Q | R) --> (P & Q) | R"; by tac; result(); -goal thy "?p : (P | Q) & R --> (P & R) | (Q & R)"; +Goal "?p : (P | Q) & R --> (P & R) | (Q & R)"; by tac; result(); -goal thy "?p : (P & R) | (Q & R) --> (P | Q) & R"; +Goal "?p : (P & R) | (Q & R) --> (P | Q) & R"; by tac; result(); writeln"Laws involving implication"; -goal thy "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"; +Goal "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"; by tac; result(); -goal thy "?p : (P & Q --> R) <-> (P--> (Q-->R))"; +Goal "?p : (P & Q --> R) <-> (P--> (Q-->R))"; by tac; result(); -goal thy "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"; +Goal "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"; by tac; result(); -goal thy "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"; +Goal "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"; by tac; result(); -goal thy "?p : (P --> Q & R) <-> (P-->Q) & (P-->R)"; +Goal "?p : (P --> Q & R) <-> (P-->Q) & (P-->R)"; by tac; result(); @@ -78,22 +78,22 @@ writeln"Propositions-as-types"; (*The combinator K*) -goal thy "?p : P --> (Q --> P)"; +Goal "?p : P --> (Q --> P)"; by tac; result(); (*The combinator S*) -goal thy "?p : (P-->Q-->R) --> (P-->Q) --> (P-->R)"; +Goal "?p : (P-->Q-->R) --> (P-->Q) --> (P-->R)"; by tac; result(); (*Converse is classical*) -goal thy "?p : (P-->Q) | (P-->R) --> (P --> Q | R)"; +Goal "?p : (P-->Q) | (P-->R) --> (P --> Q | R)"; by tac; result(); -goal thy "?p : (P-->Q) --> (~Q --> ~P)"; +Goal "?p : (P-->Q) --> (~Q --> ~P)"; by tac; result(); @@ -101,39 +101,39 @@ writeln"Schwichtenberg's examples (via T. Nipkow)"; (* stab-imp *) -goal thy "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"; +Goal "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"; by tac; result(); (* stab-to-peirce *) -goal thy "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \ +Goal "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \ \ --> ((P --> Q) --> P) --> P"; by tac; result(); (* peirce-imp1 *) -goal thy "?p : (((Q --> R) --> Q) --> Q) \ +Goal "?p : (((Q --> R) --> Q) --> Q) \ \ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"; by tac; result(); (* peirce-imp2 *) -goal thy "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"; +Goal "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"; by tac; result(); (* mints *) -goal thy "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"; +Goal "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"; by tac; result(); (* mints-solovev *) -goal thy "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"; +Goal "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"; by tac; result(); (* tatsuta *) -goal thy "?p : (((P7 --> P1) --> P10) --> P4 --> P5) \ +Goal "?p : (((P7 --> P1) --> P10) --> P4 --> P5) \ \ --> (((P8 --> P2) --> P9) --> P3 --> P10) \ \ --> (P1 --> P8) --> P6 --> P7 \ \ --> (((P3 --> P2) --> P9) --> P4) \ @@ -142,7 +142,7 @@ result(); (* tatsuta1 *) -goal thy "?p : (((P8 --> P2) --> P9) --> P3 --> P10) \ +Goal "?p : (((P8 --> P2) --> P9) --> P3 --> P10) \ \ --> (((P3 --> P2) --> P9) --> P4) \ \ --> (((P6 --> P1) --> P2) --> P9) \ \ --> (((P7 --> P1) --> P10) --> P4 --> P5) \