Theorem: Groupoid.right_cancel_id (Complexes/Structures/Groupoid.lean)

State before:
S : Sort u_1
G : Groupoid S
X Y Z : S
g g' : X ⟶ Y
h h' : Y ⟶ Z
e : X ⟶ X
⊢ g = e ≫ g ↔ 𝟙 X = e
Tactic:
have := right_cancel (𝟙 X) e g
State after:
S : Sort u_1
G : Groupoid S
X Y Z : S
g g' : X ⟶ Y
h h' : Y ⟶ Z
e : X ⟶ X
this : 𝟙 X ≫ g = e ≫ g ↔ 𝟙 X = e
⊢ g = e ≫ g ↔ 𝟙 X = e

State before:
S : Sort u_1
G : Groupoid S
X Y Z : S
g g' : X ⟶ Y
h h' : Y ⟶ Z
e : X ⟶ X
this : 𝟙 X ≫ g = e ≫ g ↔ 𝟙 X = e
⊢ g = e ≫ g ↔ 𝟙 X = e
Tactic:
simp at this
State after:
S : Sort u_1
G : Groupoid S
X Y Z : S
g g' : X ⟶ Y
h h' : Y ⟶ Z
e : X ⟶ X
this : g = e ≫ g ↔ 𝟙 X = e
⊢ g = e ≫ g ↔ 𝟙 X = e

State before:
S : Sort u_1
G : Groupoid S
X Y Z : S
g g' : X ⟶ Y
h h' : Y ⟶ Z
e : X ⟶ X
this : g = e ≫ g ↔ 𝟙 X = e
⊢ g = e ≫ g ↔ 𝟙 X = e
Tactic:
assumption
State after:
no goals