R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ image (fun n => coeff 1 n) (support 1) ⊆ {1}
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ frange 1 ⊆ {1}
simp only [frange]
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ ∀ (x : ℕ), x ∈ support 1 → coeff 1 x ∈ {1}
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ image (fun n => coeff 1 n) (support 1) ⊆ {1}
rw [Finset.image_subset_iff]
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ ∀ (x : ℕ), ¬(if x = 0 then 1 else 0) = 0 → (if x = 0 then 1 else 0) = 1
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ ∀ (x : ℕ), x ∈ support 1 → coeff 1 x ∈ {1}
simp only [mem_support_iff, ne_eq, mem_singleton, ← C_1, coeff_C]
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
n : ℕ
hn : ¬(if n = 0 then 1 else 0) = 0
⊢ (if n = 0 then 1 else 0) = 1
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
⊢ ∀ (x : ℕ), ¬(if x = 0 then 1 else 0) = 0 → (if x = 0 then 1 else 0) = 1
intro n hn
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
n : ℕ
hn : n = 0 ∧ ¬1 = 0
⊢ (if n = 0 then 1 else 0) = 1
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
n : ℕ
hn : ¬(if n = 0 then 1 else 0) = 0
⊢ (if n = 0 then 1 else 0) = 1
simp only [exists_prop, ite_eq_right_iff, not_forall] at hn
no goals
R : Type u
S : Type ?u.46907
inst✝ : Semiring R
n : ℕ
hn : n = 0 ∧ ¬1 = 0
⊢ (if n = 0 then 1 else 0) = 1
simp [hn]