14 lines
791 B
Text
14 lines
791 B
Text
∀ (A : Type) [_inst_1 : has_add A] [_inst_2 : has_zero A] [_inst_3 : has_lt A] (a : A),
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@eq A a (@add A _inst_1 (@zero A _inst_2) (@zero A _inst_2)) →
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@gt A _inst_3 (@add A _inst_1 a a) (@zero A _inst_2) :
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Prop
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int → int : Type
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λ (x : int),
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@add int (@distrib.to_has_add int (@ring.to_distrib int (@comm_ring.to_ring int int_comm_ring))) x
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(@one int (@monoid.to_has_one int (@ring.to_monoid int (@comm_ring.to_ring int int_comm_ring)))) :
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int → int
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λ (A : Type) (a b c d : A) (H1 : @eq A a b) (H2 : @eq A b c) (H3 : @eq A d c),
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have this : @eq A a c, from @eq.trans A a b c H1 H2,
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have H3' : @eq A c d, from @eq.symm A d c H3,
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show @eq A a d, from @eq.trans A a c d this H3' :
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∀ (A : Type) (a b c d : A), @eq A a b → @eq A b c → @eq A d c → @eq A a d
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