Theorem: b₁_hi_of_round_le (Fl.lean)

State before:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
round_le : round (a - b) ≤ a - b
⊢ trunc n (round (a - b) - (a - b)) = round (a - b) - (a - b)
Tactic:
rewrite [round_eq_trunc_of_le npos hfaithful₁ round_le]
State after:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
round_le : round (a - b) ≤ a - b
⊢ trunc n (trunc n (a - b) - (a - b)) = trunc n (a - b) - (a - b)

State before:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
round_le : round (a - b) ≤ a - b
⊢ trunc n (trunc n (a - b) - (a - b)) = trunc n (a - b) - (a - b)
Tactic:
rewrite [tsub_eq_zero_of_le (trunc_le n (a - b))]
State after:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
round_le : round (a - b) ≤ a - b
⊢ trunc n 0 = 0

State before:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
round_le : round (a - b) ≤ a - b
⊢ trunc n 0 = 0
Tactic:
exact trunc_zero n
State after:
no goals