Theorems · Definition · order theory
LinearOrderedCommGroupWithZero.fst
(α : Type u_1) →
(β : Type u_2) →
[inst : LinearOrderedCommGroupWithZero α] →
[inst_1 : LinearOrderedCommGroupWithZero β] → WithZero (Lex (αˣ × βˣ)) →*₀o αGiven linearly ordered groups with zero M, N, the natural projection ordered homomorphism from
WithZero (Mˣ ×ₗ Nˣ) to M, which is the linearly ordered group with zero that can be identified
as their product.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Lex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- MonoidWithZeroHomproof · cited by 704
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MulEquiv.symmproof · cited by 482
- Lexstatement and proof · cited by 370
- MulEquiv.toMonoidHomproof · cited by 126
- OrderMonoidWithZeroHomstatement · cited by 48
- WithZero.map'proof · cited by 45
- MonoidWithZeroHom.compproof · cited by 34
- MonoidWithZeroHom.fstproof · cited by 10
- toLexMulEquivproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroupWithZero.fst_applystatement and proof · cited by 1
- LinearOrderedCommGroupWithZero.fst_comp_inlstatement and proof · cited by 0