2015-11-07 05:02:04 +00:00
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-- Rewriting with (tmp)-local hypotheses
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import logic.quantifiers
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2015-11-16 19:01:53 +00:00
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namespace tst
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2015-11-07 21:39:31 +00:00
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attribute congr_forall [congr]
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attribute congr_imp [congr]
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2015-11-16 19:01:53 +00:00
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end tst
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2015-11-07 21:39:31 +00:00
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2015-11-07 05:02:04 +00:00
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universe l
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2015-11-16 19:01:53 +00:00
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constants (T : Type.{l}) (P Q : T → Prop)
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2015-11-07 05:02:04 +00:00
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set_option simplify.max_steps 50000
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constants (x y : T)
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2015-11-16 19:01:53 +00:00
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-- TODO(Daniel): the following is looping...
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#simplify iff tst 0 x = y → x = y
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#simplify iff tst 0 T → x = y → x = y
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#simplify iff tst 0 ∀ z : T, x = z → x = y
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#simplify iff tst 0 ∀ z : T, z = x → x = z
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#simplify iff tst 0 ∀ (z w : T), x = y → x = y
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#simplify iff tst 0 ∀ (z w : T), x = y → P x
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#simplify iff tst 0 ∀ (H : ∀ x, P x ↔ Q x), P x
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#simplify iff tst 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x) (q : Prop), P x
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#simplify iff tst 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x), p ∨ P x
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#simplify iff tst 0 (∀ (x : T), P x ↔ Q x) → P x
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#simplify iff tst 0 (∀ (x : T), P x ↔ Q x) → P x
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#simplify iff tst 0 ∀ (x y : T), (∀ (x : T), P x ↔ Q x) → P x
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#simplify iff tst 0 ∀ (x z : T), x = z → (∀ (w : T), P w ↔ Q w) → P x
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