# norm_num extension for equalities #

theorem Mathlib.Meta.NormNum.isNat_eq_false {α : Type u_1} [] [] {a : α} {b : α} {a' : } {b' : } :
Nat.beq a' b' = false¬a = b
theorem Mathlib.Meta.NormNum.isInt_eq_false {α : Type u_1} [Ring α] [] {a : α} {b : α} {a' : } {b' : } :
decide (a' = b') = false¬a = b
theorem Mathlib.Meta.NormNum.Rat.invOf_denom_swap {α : Type u_1} [Ring α] (n₁ : ) (n₂ : ) (a₁ : α) (a₂ : α) [] [] :
n₁ * a₁ = n₂ * a₂ n₁ * a₂ = n₂ * a₁
theorem Mathlib.Meta.NormNum.isRat_eq_false {α : Type u_1} [Ring α] [] {a : α} {b : α} {na : } {nb : } {da : } {db : } :
decide (Int.mul na () = Int.mul nb ()) = false¬a = b

The norm_num extension which identifies expressions of the form a = b, such that norm_num successfully recognises both a and b.

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def Mathlib.Meta.NormNum.evalEq.intArm {v : Lean.Level} {β : Q(Type v)} (e : Q(«$β»)) (u : Lean.Level) (α : let u := u; Q(Type u)) (a : Q(«$α»)) (b : Q(«$α»)) (ra : ) (rb : ) (rα : Q(Ring «$α»)) :
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def Mathlib.Meta.NormNum.evalEq.ratArm {v : Lean.Level} {β : Q(Type v)} (e : Q(«$β»)) (u : Lean.Level) (α : let u := u; Q(Type u)) (a : Q(«$α»)) (b : Q(«$α»)) (ra : ) (rb : ) (dα : Q(DivisionRing «$α»)) :
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