no goals
R : Type u
inst✝² : Semiring R
ι : Type v
dec_ι : DecidableEq ι
M : Type u_1
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
A✝ A : ι → Submodule R M
i j : ι
hij : i ≠ j
h : Set.univ = {i, j}
hi : IsInternal A
⊢ iSup A = A i ⊔ A j
rw [← sSup_pair, iSup, ← Set.image_univ, h, Set.image_insert_eq, Set.image_singleton]