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92 lemma conjunction_imp: |
92 lemma conjunction_imp: |
93 includes meta_conjunction_syntax |
93 includes meta_conjunction_syntax |
94 shows "(PROP A && PROP B ==> PROP C) == (PROP A ==> PROP B ==> PROP C)" |
94 shows "(PROP A && PROP B ==> PROP C) == (PROP A ==> PROP B ==> PROP C)" |
95 proof |
95 proof |
96 assume r: "PROP A && PROP B ==> PROP C" |
96 assume r: "PROP A && PROP B ==> PROP C" |
97 assume "PROP A" and "PROP B" |
97 assume ab: "PROP A" "PROP B" |
98 show "PROP C" by (rule r) - |
98 show "PROP C" |
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99 proof (rule r) |
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100 from ab show "PROP A && PROP B" . |
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101 qed |
99 next |
102 next |
100 assume r: "PROP A ==> PROP B ==> PROP C" |
103 assume r: "PROP A ==> PROP B ==> PROP C" |
101 assume conj: "PROP A && PROP B" |
104 assume conj: "PROP A && PROP B" |
102 show "PROP C" |
105 show "PROP C" |
103 proof (rule r) |
106 proof (rule r) |