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tactic.​monotonicity.​lemmas

tactic.​monotonicity.​lemmas

source
lt_of_mul_lt_mul_neg_right
mul_mono_nonneg
mul_mono_nonpos
nat.​sub_mono_left_strict
nat.​sub_mono_right_strict
source
theorem mul_mono_nonneg {α : Type u_1} {x y z : α} [ordered_semiring α] :
0 ≤ z → x ≤ y → x * z ≤ y * z

source
theorem lt_of_mul_lt_mul_neg_right {α : Type u_1} {a b c : α} [linear_ordered_ring α] :
a * c < b * c → c ≤ 0 → b < a

source
theorem mul_mono_nonpos {α : Type u_1} {x y z : α} [linear_ordered_ring α] :
z ≤ 0 → y ≤ x → x * z ≤ y * z

source
theorem nat.​sub_mono_left_strict {x y z : ℕ} :
z ≤ x → x < y → x - z < y - z

source
theorem nat.​sub_mono_right_strict {x y z : ℕ} :
x ≤ z → y < x → z - x < z - y

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