author | wenzelm |
Fri, 10 Oct 1997 18:17:17 +0200 | |
changeset 3839 | 56544d061e1d |
parent 2073 | fb0655539d05 |
permissions | -rw-r--r-- |
2073
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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(* Title: LK/ex/quant |
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New unified treatment of sequent calculi by Sara Kalvala
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ID: $Id$ |
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New unified treatment of sequent calculi by Sara Kalvala
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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New unified treatment of sequent calculi by Sara Kalvala
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Copyright 1992 University of Cambridge |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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Classical sequent calculus: examples with quantifiers. |
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New unified treatment of sequent calculi by Sara Kalvala
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*) |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"LK/ex/quant: Examples with quantifiers"; |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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goal LK.thy "|- (ALL x. P) <-> P"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
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13 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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14 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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3839 | 16 |
goal LK.thy "|- (ALL x y. P(x,y)) <-> (ALL y x. P(x,y))"; |
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New unified treatment of sequent calculi by Sara Kalvala
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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18 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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3839 | 20 |
goal LK.thy "ALL u. P(u), ALL v. Q(v) |- ALL u v. P(u) & Q(v)"; |
2073
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New unified treatment of sequent calculi by Sara Kalvala
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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22 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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23 |
|
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"Permutation of existential quantifier."; |
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goal LK.thy "|- (EX x y. P(x,y)) <-> (EX y x. P(x,y))"; |
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New unified treatment of sequent calculi by Sara Kalvala
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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3839 | 29 |
goal LK.thy "|- (ALL x. P(x) & Q(x)) <-> (ALL x. P(x)) & (ALL x. Q(x))"; |
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New unified treatment of sequent calculi by Sara Kalvala
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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(*Converse is invalid*) |
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goal LK.thy "|- (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x)|Q(x))"; |
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"Pushing ALL into an implication."; |
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goal LK.thy "|- (ALL x. P --> Q(x)) <-> (P --> (ALL x. Q(x)))"; |
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New unified treatment of sequent calculi by Sara Kalvala
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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3839 | 46 |
goal LK.thy "|- (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"; |
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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goal LK.thy "|- (EX x. P) <-> P"; |
fb0655539d05
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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53 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"Distribution of EX over disjunction."; |
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New unified treatment of sequent calculi by Sara Kalvala
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goal LK.thy "|- (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"; |
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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(*5 secs*) |
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(*Converse is invalid*) |
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goal LK.thy "|- (EX x. P(x) & Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"; |
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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65 |
result(); |
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writeln"Harder examples: classical theorems."; |
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69 |
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3839 | 70 |
goal LK.thy "|- (EX x. P-->Q(x)) <-> (P --> (EX x. Q(x)))"; |
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by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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result(); |
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(*3 secs*) |
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3839 | 76 |
goal LK.thy "|- (EX x. P(x)-->Q) <-> (ALL x. P(x)) --> Q"; |
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77 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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result(); |
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paulson
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(*5 secs*) |
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3839 | 82 |
goal LK.thy "|- (ALL x. P(x)) | Q <-> (ALL x. P(x) | Q)"; |
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83 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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84 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"Basic test of quantifier reasoning"; |
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88 |
goal LK.thy |
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"|- (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"; |
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90 |
by (fast_tac LK_pack 1); |
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result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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goal LK.thy "|- (ALL x. Q(x)) --> (EX x. Q(x))"; |
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95 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
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96 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
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98 |
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New unified treatment of sequent calculi by Sara Kalvala
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writeln"The following are invalid!"; |
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100 |
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(*INVALID*) |
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102 |
goal LK.thy "|- (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"; |
fb0655539d05
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103 |
by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected"; |
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104 |
(*Check that subgoals remain: proof failed.*) |
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New unified treatment of sequent calculi by Sara Kalvala
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105 |
getgoal 1; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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106 |
|
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
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107 |
(*INVALID*) |
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108 |
goal LK.thy "|- (EX x. Q(x)) --> (ALL x. Q(x))"; |
fb0655539d05
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109 |
by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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110 |
getgoal 1; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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111 |
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3839 | 112 |
goal LK.thy "|- P(?a) --> (ALL x. P(x))"; |
2073
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113 |
by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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114 |
(*Check that subgoals remain: proof failed.*) |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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115 |
getgoal 1; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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116 |
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3839 | 117 |
goal LK.thy "|- (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"; |
2073
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New unified treatment of sequent calculi by Sara Kalvala
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118 |
by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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119 |
getgoal 1; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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120 |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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121 |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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122 |
writeln"Back to things that are provable..."; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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123 |
|
3839 | 124 |
goal LK.thy "|- (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"; |
2073
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New unified treatment of sequent calculi by Sara Kalvala
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125 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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126 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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127 |
|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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128 |
(*An example of why exR should be delayed as long as possible*) |
3839 | 129 |
goal LK.thy "|- (P--> (EX x. Q(x))) & P--> (EX x. Q(x))"; |
2073
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130 |
by (fast_tac LK_pack 1); |
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paulson
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131 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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132 |
|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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133 |
writeln"Solving for a Var"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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134 |
goal LK.thy |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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135 |
"|- (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"; |
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136 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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137 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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|
138 |
|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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|
139 |
|
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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140 |
writeln"Principia Mathematica *11.53"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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141 |
goal LK.thy |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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|
142 |
"|- (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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|
143 |
by (fast_tac LK_pack 1); |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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|
144 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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|
145 |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
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146 |
|
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147 |
writeln"Principia Mathematica *11.55"; |
3839 | 148 |
goal LK.thy "|- (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"; |
2073
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149 |
by (fast_tac LK_pack 1); |
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150 |
result(); |
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151 |
|
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152 |
writeln"Principia Mathematica *11.61"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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changeset
|
153 |
goal LK.thy |
fb0655539d05
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paulson
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154 |
"|- (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
155 |
by (fast_tac LK_pack 1); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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156 |
result(); |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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157 |
|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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158 |
writeln"Reached end of file."; |
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New unified treatment of sequent calculi by Sara Kalvala
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159 |
|
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160 |
(*21 August 88: loaded in 45.7 secs*) |