2015-11-05 05:53:12 +00:00
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/- Basic pi congruence -/
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import logic.connectives logic.quantifiers
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namespace pi_congr1
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constants (p1 q1 p2 q2 p3 q3 : Prop) (H1 : p1 ↔ q1) (H2 : p2 ↔ q2) (H3 : p3 ↔ q3)
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2015-11-17 00:00:00 +00:00
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2015-11-16 19:01:53 +00:00
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attribute congr_forall [congr]
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attribute congr_imp [congr]
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attribute H1 [simp]
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attribute H2 [simp]
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attribute H3 [simp]
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2015-11-05 05:53:12 +00:00
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2015-11-17 00:00:00 +00:00
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#simplify iff env 1 p1 -- Broken?
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#simplify iff env 1 p1 → p2
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#simplify iff env 1 p1 → p2 → p3
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2015-11-05 05:53:12 +00:00
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end pi_congr1
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namespace pi_congr2
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universe l
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constants (T : Type.{l}) (P Q : T → Prop) (H : ∀ (x : T), P x ↔ Q x)
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2015-11-17 00:00:00 +00:00
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attribute congr_forall [congr]
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2015-11-16 19:01:53 +00:00
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attribute H [simp]
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2015-11-17 00:00:00 +00:00
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2015-11-05 05:53:12 +00:00
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constant (x : T)
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2015-11-17 00:00:00 +00:00
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#simplify iff env 1 (∀ (x : T), P x)
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2015-11-05 05:53:12 +00:00
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end pi_congr2
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