Theorems · Theorem · real analysis
CauSeq.mul_not_equiv_zero
∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
[inst_3 : Ring β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] {f g : CauSeq β abv}, ¬f ≈ 0 → ¬g ≈ 0 → ¬f * g ≈ 0- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- sub_zeroproof · cited by 938
- mul_posproof · cited by 374
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- CauSeqstatement and proof · cited by 189
- IsAbsoluteValuestatement and proof · cited by 160
Cited by1
Results whose statement or proof uses this declaration.
- PadicSeq.norm_mulproof · cited by 0