this : 1 + sqrt 5 ≠ 0
⊢ φ⁻¹ = -ψ
⊢ φ⁻¹ = -ψ
have : 1 + Real.sqrt 5 ≠ 0 := ne_of_gt (add_pos (by norm_num) <| Real.sqrt_pos.mpr (by norm_num))
this : 1 + sqrt 5 ≠ 0
⊢ 2 * 2 = sqrt 5 * sqrt 5 - 1
this : 1 + sqrt 5 ≠ 0
⊢ φ⁻¹ = -ψ
field_simp [sub_mul, mul_add]
no goals
this : 1 + sqrt 5 ≠ 0
⊢ 2 * 2 = sqrt 5 * sqrt 5 - 1
norm_num
no goals
⊢ 0 < 1
norm_num
no goals
⊢ 0 < 5
norm_num