case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ abs a ≤ abs b
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ ‖a‖ ≤ ‖b‖
apply solid
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ a ⊔ -a ≤ abs b
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ abs a ≤ abs b
rw [abs_eq_sup_neg]
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ - -a ⊔ -a ≤ abs b
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ a ⊔ -a ≤ abs b
nth_rw 1 [← neg_neg a]
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ abs b
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ - -a ⊔ -a ≤ abs b
rw [← neg_inf_eq_sup_neg]
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ b ⊔ -b
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ abs b
rw [abs_eq_sup_neg]
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ - -b ⊔ -b
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ b ⊔ -b
nth_rw 1 [← neg_neg b]
no goals
case a
α : Type u_1
inst✝ : NormedLatticeAddCommGroup α
a b : α
h : b ⊓ -b ≤ a ⊓ -a
⊢ -(-a ⊓ a) ≤ - -b ⊔ -b
rwa [← neg_inf_eq_sup_neg, neg_le_neg_iff, @inf_comm _ _ _ b, @inf_comm _ _ _ a]