case h.e'_2.h.e'_2.h.a
R : Type u
S : Type v
T : Type w
inst✝⁴ : NonUnitalNonAssocSemiring R
M : Subsemigroup R
inst✝³ : NonUnitalNonAssocSemiring S
inst✝² : NonUnitalNonAssocSemiring T
F : Type u_1
G : Type ?u.101174
inst✝¹ : NonUnitalRingHomClass F R S
inst✝ : NonUnitalRingHomClass G S T
s✝ : NonUnitalSubsemiring R
f : F
s : NonUnitalSubsemiring R
y : S
x✝ : R
⊢ x✝ ∈ s ∧ ↑f x✝ = y ↔ ∃ x, ↑f x✝ = y
R : Type u
S : Type v
T : Type w
inst✝⁴ : NonUnitalNonAssocSemiring R
M : Subsemigroup R
inst✝³ : NonUnitalNonAssocSemiring S
inst✝² : NonUnitalNonAssocSemiring T
F : Type u_1
G : Type ?u.101174
inst✝¹ : NonUnitalRingHomClass F R S
inst✝ : NonUnitalRingHomClass G S T
s✝ : NonUnitalSubsemiring R
f : F
s : NonUnitalSubsemiring R
y : S
⊢ y ∈ map f s ↔ ∃ x, x ∈ s ∧ ↑f x = y
convert Set.mem_image_iff_bex
no goals
case h.e'_2.h.e'_2.h.a
R : Type u
S : Type v
T : Type w
inst✝⁴ : NonUnitalNonAssocSemiring R
M : Subsemigroup R
inst✝³ : NonUnitalNonAssocSemiring S
inst✝² : NonUnitalNonAssocSemiring T
F : Type u_1
G : Type ?u.101174
inst✝¹ : NonUnitalRingHomClass F R S
inst✝ : NonUnitalRingHomClass G S T
s✝ : NonUnitalSubsemiring R
f : F
s : NonUnitalSubsemiring R
y : S
x✝ : R
⊢ x✝ ∈ s ∧ ↑f x✝ = y ↔ ∃ x, ↑f x✝ = y
simp