case mp
C : Type u_1
inst✝ : Category C
⊢ IsIdempotentComplete Cᵒᵖ → IsIdempotentComplete C

case mpr
C : Type u_1
inst✝ : Category C
⊢ IsIdempotentComplete C → IsIdempotentComplete Cᵒᵖ
C : Type u_1
inst✝ : Category C
⊢ IsIdempotentComplete Cᵒᵖ ↔ IsIdempotentComplete C
constructor
no goals
case mp
C : Type u_1
inst✝ : Category C
⊢ IsIdempotentComplete Cᵒᵖ → IsIdempotentComplete C
exact isIdempotentComplete_of_isIdempotentComplete_opposite
case mpr
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete Cᵒᵖ
case mpr
C : Type u_1
inst✝ : Category C
⊢ IsIdempotentComplete C → IsIdempotentComplete Cᵒᵖ
intro h
case mpr.h
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete Cᵒᵖᵒᵖ
case mpr
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete Cᵒᵖ
apply isIdempotentComplete_of_isIdempotentComplete_opposite
case mpr.h
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete C
case mpr.h
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete Cᵒᵖᵒᵖ
rw [isIdempotentComplete_iff_of_equivalence (opOpEquivalence C)]
no goals
case mpr.h
C : Type u_1
inst✝ : Category C
h : IsIdempotentComplete C
⊢ IsIdempotentComplete C
exact h