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Mathlib.Init.Data.Quot

Quotient types #

These are ported from the Lean 3 standard library file init/data/quot.lean.

inductive EqvGen {α : Type u} (r : ααProp) :
ααProp

EqvGen r is the equivalence relation generated by r.

Instances For
    theorem EqvGen.is_equivalence {α : Type u} (r : ααProp) :
    def EqvGen.Setoid {α : Type u} (r : ααProp) :

    EqvGen.Setoid r is the setoid generated by a relation r.

    The motivation for this definition is that Quot r behaves like Quotient (EqvGen.Setoid r), see for example Quot.exact and Quot.EqvGen_sound.

    Equations
    Instances For
      theorem Quot.exact {α : Type u} (r : ααProp) {a : α} {b : α} (H : Quot.mk r a = Quot.mk r b) :
      EqvGen r a b
      theorem Quot.EqvGen_sound {α : Type u} {r : ααProp} {a : α} {b : α} (H : EqvGen r a b) :
      Quot.mk r a = Quot.mk r b
      instance Quotient.decidableEq {α : Sort u} {s : Setoid α} [d : (a b : α) → Decidable (a b)] :
      Equations
      • One or more equations did not get rendered due to their size.