Theorems · Theorem · order theory
Mathlib.Meta.Positivity.div_ne_zero_of_ne_zero_of_pos
∀ {α : Type u_4} [inst : GroupWithZero α] [inst_1 : PartialOrder α] {a b : α}, a ≠ 0 → 0 < b → a / b ≠ 0- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZeroPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.ne'proof · cited by 1,417
- GroupWithZerostatement and proof · cited by 691
- div_ne_zeroproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- Real.one_sub_sq_div_two_lt_cosproof · cited by 1