-- Conditional congruence import logic.connectives logic.quantifiers namespace if_congr constants {A : Type} {b c : Prop} (dec_b : decidable b) (dec_c : decidable c) {x y u v : A} (h_c : b ↔ c) (h_t : x = u) (h_e : y = v) attribute dec_b [instance] attribute dec_c [instance] attribute h_c [simp] attribute h_t [simp] attribute h_e [simp] attribute if_congr [congr] #simplify eq env 0 (ite b x y) end if_congr namespace if_ctx_simp_congr constants {A : Type} {b c : Prop} (dec_b : decidable b) {x y u v : A} (h_c : b ↔ c) (h_t : c → x = u) (h_e : ¬c → y = v) attribute dec_b [instance] attribute h_c [simp] attribute h_t [simp] attribute h_e [simp] attribute if_ctx_simp_congr [congr] #simplify eq env 0 (ite b x y) end if_ctx_simp_congr namespace if_congr_prop constants {b c x y u v : Prop} (dec_b : decidable b) (dec_c : decidable c) (h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬c → (y ↔ v)) attribute dec_b [instance] attribute dec_c [instance] attribute h_c [simp] attribute h_t [simp] attribute h_e [simp] attribute if_congr_prop [congr] #simplify iff env 0 (ite b x y) end if_congr_prop namespace if_ctx_simp_congr_prop constants (b c x y u v : Prop) (dec_b : decidable b) (h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬ c → (y ↔ v)) attribute dec_b [instance] attribute h_c [simp] attribute h_t [simp] attribute h_e [simp] attribute if_ctx_simp_congr_prop [congr] #simplify iff env 0 (ite b x y) end if_ctx_simp_congr_prop namespace if_simp_congr_prop constants (b c x y u v : Prop) (dec_b : decidable b) (h_c : b ↔ c) (h_t : x ↔ u) (h_e : y ↔ v) attribute dec_b [instance] attribute h_c [simp] attribute h_t [simp] attribute h_e [simp] attribute if_simp_congr_prop [congr] #simplify iff env 0 (ite b x y) end if_simp_congr_prop