θ : ↑I
⊢ 1 * (1 + ↑θ) ≤ 2 * ↑1
θ : ↑I
⊢ 1 * (1 + ↑(1, θ).snd) ≤ 2 * ↑(1, θ).fst
dsimp only
θ : ↑I
⊢ ↑θ + 1 ≤ 1 + 1
θ : ↑I
⊢ 1 * (1 + ↑θ) ≤ 2 * ↑1
rw [coe_one, one_mul, mul_one, add_comm, ← one_add_one_eq_two]
θ : ↑I
⊢ ↑θ ≤ 1
θ : ↑I
⊢ ↑θ + 1 ≤ 1 + 1
simp only [add_le_add_iff_right]
no goals
θ : ↑I
⊢ ↑θ ≤ 1
exact le_one _