Theorem: a₁_lo_of_lt_round (Fl.lean)

State before:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
lt_round : a + b < round (a + b)
⊢ trunc n (a + b - round (a + b)) = a + b - round (a + b)
Tactic:
rewrite [round_eq_next_trunc_of_gt hfaithful₁ lt_round]
State after:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
lt_round : a + b < round (a + b)
⊢ trunc n (a + b - next n (trunc n (a + b))) = a + b - next n (trunc n (a + b))

State before:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
lt_round : a + b < round (a + b)
⊢ trunc n (a + b - next n (trunc n (a + b))) = a + b - next n (trunc n (a + b))
Tactic:
rewrite [tsub_eq_zero_of_le (Nat.le_of_lt (lt_next_trunc npos _))]
State after:
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
lt_round : a + b < round (a + b)
⊢ trunc n 0 = 0

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