rw [← hyp] at non_zero
R : Type u_1
inst✝² : Ring R
inst✝¹ : DecidableEq R
X : Type u_2
inst✝ : DecidableEq X
a : R
x₀ x₁ : X
non_zero : 0 ≠ coords [(a, x₁)] x₁
hyp : coords [(a, x₀)] = coords [(a, x₁)]
sup₀ : support [(a, x₀)] = [x₀]
c₁ : coords [(a, x₁)] x₁ = a
⊢ x₀ = x₁
R : Type u_1
inst✝² : Ring R
inst✝¹ : DecidableEq R
X : Type u_2
inst✝ : DecidableEq X
a : R
x₀ x₁ : X
non_zero : 0 ≠ coords [(a, x₀)] x₁
hyp : coords [(a, x₀)] = coords [(a, x₁)]
sup₀ : support [(a, x₀)] = [x₀]
c₁ : coords [(a, x₁)] x₁ = a
⊢ x₀ = x₁