File: Mathlib/Tactic/CC/Lemmas.lean

full_name: Mathlib.Tactic.CC.iff_eq_of_eq_true_left
code: theorem iff_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a ↔ b) = b 
goal: (a ↔ b) = b

full_name: Mathlib.Tactic.CC.iff_eq_of_eq_true_right
code: theorem iff_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a ↔ b) = a 
goal: (a ↔ b) = a

full_name: Mathlib.Tactic.CC.iff_eq_true_of_eq
code: theorem iff_eq_true_of_eq {a b : Prop} (h : a = b) : (a ↔ b) = True 
goal: (a ↔ b) = True

full_name: Mathlib.Tactic.CC.and_eq_of_eq_true_left
code: theorem and_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a ∧ b) = b 
goal: (a ∧ b) = b

full_name: Mathlib.Tactic.CC.and_eq_of_eq_true_right
code: theorem and_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a ∧ b) = a 
goal: (a ∧ b) = a

full_name: Mathlib.Tactic.CC.and_eq_of_eq_false_left
code: theorem and_eq_of_eq_false_left {a b : Prop} (h : a = False) : (a ∧ b) = False 
goal: (a ∧ b) = False

full_name: Mathlib.Tactic.CC.and_eq_of_eq_false_right
code: theorem and_eq_of_eq_false_right {a b : Prop} (h : b = False) : (a ∧ b) = False 
goal: (a ∧ b) = False

full_name: Mathlib.Tactic.CC.and_eq_of_eq
code: theorem and_eq_of_eq {a b : Prop} (h : a = b) : (a ∧ b) = a 
goal: (a ∧ b) = a

full_name: Mathlib.Tactic.CC.or_eq_of_eq_true_left
code: theorem or_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a ∨ b) = True 
goal: (a ∨ b) = True

full_name: Mathlib.Tactic.CC.or_eq_of_eq_true_right
code: theorem or_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a ∨ b) = True 
goal: (a ∨ b) = True

full_name: Mathlib.Tactic.CC.or_eq_of_eq_false_left
code: theorem or_eq_of_eq_false_left {a b : Prop} (h : a = False) : (a ∨ b) = b 
goal: (a ∨ b) = b

full_name: Mathlib.Tactic.CC.or_eq_of_eq_false_right
code: theorem or_eq_of_eq_false_right {a b : Prop} (h : b = False) : (a ∨ b) = a 
goal: (a ∨ b) = a

full_name: Mathlib.Tactic.CC.or_eq_of_eq
code: theorem or_eq_of_eq {a b : Prop} (h : a = b) : (a ∨ b) = a 
goal: (a ∨ b) = a

full_name: Mathlib.Tactic.CC.imp_eq_of_eq_true_left
code: theorem imp_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a → b) = b 
goal: (a → b) = b

full_name: Mathlib.Tactic.CC.imp_eq_of_eq_true_right
code: theorem imp_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a → b) = True 
goal: (a → b) = True

full_name: Mathlib.Tactic.CC.imp_eq_of_eq_false_left
code: theorem imp_eq_of_eq_false_left {a b : Prop} (h : a = False) : (a → b) = True 
goal: (a → b) = True

full_name: Mathlib.Tactic.CC.imp_eq_of_eq_false_right
code: theorem imp_eq_of_eq_false_right {a b : Prop} (h : b = False) : (a → b) = Not a 
goal: (a → b) = ¬a

full_name: Mathlib.Tactic.CC.not_imp_eq_of_eq_false_right
code: theorem not_imp_eq_of_eq_false_right {a b : Prop} (h : b = False) : (Not a → b) = a 
goal: (¬a → b) = a

full_name: Mathlib.Tactic.CC.imp_eq_true_of_eq
code: theorem imp_eq_true_of_eq {a b : Prop} (h : a = b) : (a → b) = True 
goal: (a → b) = True

full_name: Mathlib.Tactic.CC.not_eq_of_eq_true
code: theorem not_eq_of_eq_true {a : Prop} (h : a = True) : Not a = False 
goal: (¬a) = False

full_name: Mathlib.Tactic.CC.not_eq_of_eq_false
code: theorem not_eq_of_eq_false {a : Prop} (h : a = False) : Not a = True 
goal: (¬a) = True

full_name: Mathlib.Tactic.CC.false_of_a_eq_not_a
code: theorem false_of_a_eq_not_a {a : Prop} (h : a = Not a) : False 
goal: False

full_name: Mathlib.Tactic.CC.if_eq_of_eq_true
code: theorem if_eq_of_eq_true {c : Prop} [d : Decidable c] {α : Sort u} (t e : α) (h : c = True) :
    @ite α c d t e = t 
goal: (if c then t else e) = t

full_name: Mathlib.Tactic.CC.if_eq_of_eq_false
code: theorem if_eq_of_eq_false {c : Prop} [d : Decidable c] {α : Sort u} (t e : α) (h : c = False) :
    @ite α c d t e = e 
goal: (if c then t else e) = e

full_name: Mathlib.Tactic.CC.if_eq_of_eq
code: theorem if_eq_of_eq (c : Prop) [d : Decidable c] {α : Sort u} {t e : α} (h : t = e) :
    @ite α c d t e = t 
goal: (if c then t else e) = t

full_name: Mathlib.Tactic.CC.eq_true_of_and_eq_true_left
code: theorem eq_true_of_and_eq_true_left {a b : Prop} (h : (a ∧ b) = True) : a = True 
goal: a = True

full_name: Mathlib.Tactic.CC.eq_true_of_and_eq_true_right
code: theorem eq_true_of_and_eq_true_right {a b : Prop} (h : (a ∧ b) = True) : b = True 
goal: b = True

full_name: Mathlib.Tactic.CC.eq_false_of_or_eq_false_left
code: theorem eq_false_of_or_eq_false_left {a b : Prop} (h : (a ∨ b) = False) : a = False 
goal: a = False

full_name: Mathlib.Tactic.CC.eq_false_of_or_eq_false_right
code: theorem eq_false_of_or_eq_false_right {a b : Prop} (h : (a ∨ b) = False) : b = False 
goal: b = False

full_name: Mathlib.Tactic.CC.eq_false_of_not_eq_true
code: theorem eq_false_of_not_eq_true {a : Prop} (h : Not a = True) : a = False 
goal: a = False

full_name: Mathlib.Tactic.CC.eq_true_of_not_eq_false
code: theorem eq_true_of_not_eq_false {a : Prop} (h : Not a = False) : a = True 
goal: a = True