26 lines
734 B
Text
26 lines
734 B
Text
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import tactic
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import macros
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definition bracket (A : Type) : Bool :=
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∀ p : Bool, (A → p) → p
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rewrite_set basic
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add_rewrite imp_truel imp_truer imp_id eq_id : basic
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set_option simp_tac::assumptions false
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theorem bracket_eq (x : Bool) : bracket x = x
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:= boolext
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(assume H : ∀ p : Bool, (x → p) → p,
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(have ((x → x) → x) = x : by simp basic) ◂ H x)
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(assume H : x,
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take p,
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assume Hxp : x → p,
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Hxp H)
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add_rewrite bracket_eq eq_id
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theorem coerce (a b : Bool) (H : @eq Type a b) : @eq Bool a b
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:= calc a = bracket a : by simp
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... = bracket b : @subst Type a b (λ x : Type, bracket a = bracket x) (refl (bracket a)) H
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... = b : by simp
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