lean2/tests/lean/simplifier6.lean
2015-11-08 14:05:03 -08:00

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/- Basic pi congruence -/
import logic.connectives logic.quantifiers
attribute congr_forall [congr]
attribute congr_imp [congr]
namespace pi_congr1
constants (p1 q1 p2 q2 p3 q3 : Prop) (H1 : p1 ↔ q1) (H2 : p2 ↔ q2) (H3 : p3 ↔ q3)
local attribute H1 [simp]
local attribute H2 [simp]
local attribute H3 [simp]
#simplify iff 1 p1
#simplify iff 1 p1 → p2
#simplify iff 1 p1 → p2 → p3
end pi_congr1
namespace pi_congr2
universe l
constants (T : Type.{l}) (P Q : T → Prop) (H : ∀ (x : T), P x ↔ Q x)
local attribute H [simp]
constant (x : T)
#simplify iff 1 (∀ (x : T), P x)
end pi_congr2