75 lines
1.9 KiB
Text
75 lines
1.9 KiB
Text
-- Conditional congruence
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import logic.connectives logic.quantifiers
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-- TODO(dhs): add this to the library
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lemma not_false_true [simp] : (¬ false) ↔ true := sorry
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namespace if_congr
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constants {A : Type} {b c : Prop} (dec_b : decidable b) (dec_c : decidable c)
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{x y u v : A} (h_c : b ↔ c) (h_t : x = u) (h_e : y = v)
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attribute dec_b [instance]
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attribute dec_c [instance]
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attribute h_c [simp]
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attribute h_t [simp]
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attribute h_e [simp]
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attribute if_congr [congr]
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#simplify eq env 0 (ite b x y)
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end if_congr
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namespace if_ctx_simp_congr
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constants {A : Type} {b c : Prop} (dec_b : decidable b)
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{x y u v : A} (h_c : b ↔ c) (h_t : c → x = u) (h_e : ¬c → y = v)
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attribute dec_b [instance]
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attribute h_c [simp]
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attribute h_t [simp]
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attribute h_e [simp]
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attribute if_ctx_simp_congr [congr]
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#simplify eq env 0 (ite b x y)
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end if_ctx_simp_congr
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namespace if_ctx_congr_prop
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constants {b c x y u v : Prop} (dec_b : decidable b) (dec_c : decidable c)
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(h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬c → (y ↔ v))
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attribute dec_b [instance]
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attribute dec_c [instance]
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attribute h_c [simp]
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attribute h_t [simp]
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attribute h_e [simp]
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attribute if_ctx_congr_prop [congr]
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#simplify iff env 0 (ite b x y)
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end if_ctx_congr_prop
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namespace if_ctx_simp_congr_prop
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constants (b c x y u v : Prop) (dec_b : decidable b)
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(h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬ c → (y ↔ v))
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attribute dec_b [instance]
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attribute h_c [simp]
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attribute h_t [simp]
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attribute h_e [simp]
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attribute if_ctx_simp_congr_prop [congr]
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#simplify iff env 0 (ite b x y)
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end if_ctx_simp_congr_prop
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namespace if_simp_congr_prop
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constants (b c x y u v : Prop) (dec_b : decidable b)
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(h_c : b ↔ c) (h_t : x ↔ u) (h_e : y ↔ v)
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attribute dec_b [instance]
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attribute h_c [simp]
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attribute h_t [simp]
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attribute h_e [simp]
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attribute if_simp_congr_prop [congr]
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#simplify iff env 0 (ite b x y)
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end if_simp_congr_prop
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