Theorems · Definition · order theory
LinearOrderedCommGroupWithZero.inl
(α : Type u_1) →
(β : Type u_2) →
[inst : LinearOrderedCommGroupWithZero α] →
[inst_1 : LinearOrderedCommGroupWithZero β] → α →*₀o WithZero (Lex (αˣ × βˣ))Given linearly ordered groups with zero M, N, the natural inclusion ordered homomorphism from
M to WithZero (Mˣ ×ₗ Nˣ), which is the linearly ordered group with zero that can be identified
as their product.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Lex
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- 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.inlproof · cited by 13
- toLexMulEquivproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroupWithZero.inl_applystatement and proof · cited by 2
- LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗstatement · cited by 1
- LinearOrderedCommGroupWithZero.fst_comp_inlstatement · cited by 0
- LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLexstatement · cited by 0