left
n k m l p : ℕ
h_klen : k ≤ n
h_p : p.Prime
h_p_div_binom : p ∣ n.choose k
H : n.choose k = m ^ l
h_p_div_ml : p ∣ m ^ l
h_pl_div_ml : p ^ l ∣ m ^ l
h_pl_div_binom : p ^ l ∣ n.choose k
h_pl_div_fac : p ^ l ∣ n.factorial / (k.factorial * (n - k).factorial)
h_fac_div : ↑k.factorial * ↑(n - k).factorial ∣ ↑n.factorial
h_fac_div' : ↑(n - k).factorial ∣ ↑n.factorial
h_fac_div'' : ↑k.factorial ∣ ↑n.factorial / ↑(n - k).factorial
h_kfac_ne_zero : ↑k.factorial ≠ 0
h_nkfac_ne_zero : ↑(n - k).factorial ≠ 0
this : ↑k.factorial * ↑(n - k).factorial ≠ 0
⊢ ↑k.factorial * ↑(n - k).factorial = ↑k.factorial * ↑(n - k).factorial ∨ n.factorial = 0
case h
n k m l p : ℕ
h_klen : k ≤ n
h_p : p.Prime
h_p_div_binom : p ∣ n.choose k
H : n.choose k = m ^ l
h_p_div_ml : p ∣ m ^ l
h_pl_div_ml : p ^ l ∣ m ^ l
h_pl_div_binom : p ^ l ∣ n.choose k
h_pl_div_fac : p ^ l ∣ n.factorial / (k.factorial * (n - k).factorial)
h_fac_div : ↑k.factorial * ↑(n - k).factorial ∣ ↑n.factorial
h_fac_div' : ↑(n - k).factorial ∣ ↑n.factorial
h_fac_div'' : ↑k.factorial ∣ ↑n.factorial / ↑(n - k).factorial
h_kfac_ne_zero : ↑k.factorial ≠ 0
h_nkfac_ne_zero : ↑(n - k).factorial ≠ 0
this : ↑k.factorial * ↑(n - k).factorial ≠ 0
⊢ ↑k.factorial * ↑(n - k).factorial = ↑k.factorial * ↑(n - k).factorial