2015-05-01 21:26:31 +00:00
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Prop:Type
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2015-05-05 21:25:35 +00:00
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by simp;by exact sorry
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true:unit
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trivial:star
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is_true:is_unit
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false:empty
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is_false:is_empty
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2015-05-01 21:26:31 +00:00
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induction:rec
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induction_on:rec_on
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2015-05-05 21:25:35 +00:00
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2015-05-01 21:26:31 +00:00
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∨;⊎
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or.elim:sum.rec_on
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or.inl:sum.inl
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or.inr:sum.inr
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2015-05-05 21:25:35 +00:00
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or.intro_left _;sum.inl
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or.intro_right _;sum.inr
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or_resolve_right:sum_resolve_right
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or_resolve_left:sum_resolve_left
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or.swap:sum.swap
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or.rec_on:sum.rec_on
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or_of_or_of_imp_of_imp:sum_of_sum_of_imp_of_imp
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or_of_or_of_imp_left:sum_of_sum_of_imp_left
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or_of_or_of_imp_right:sum_of_sum_of_imp_right
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2015-05-01 21:26:31 +00:00
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∧;×
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and.intro:pair
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and.left:
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2015-05-05 21:25:35 +00:00
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and.elim_left:prod.pr1
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and.left:prod.pr1
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and.elim_right:prod.pr2
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and.right:prod.pr2
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∀;Π
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2015-05-01 21:26:31 +00:00
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∃;Σ
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exists.intro:sigma.mk
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2015-05-05 21:25:35 +00:00
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exists.elim:sigma.rec_on
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eq.symm:inverse
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2015-05-01 21:26:31 +00:00
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congr_arg:ap
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