Theorems · Theorem · order theory

LinearOrderedCommGroupWithZero.inl_apply

∀ (α : Type u_1) (β : Type u_2) [inst : LinearOrderedCommGroupWithZero α] [inst_1 : LinearOrderedCommGroupWithZero β]
  (a : α),
  (LinearOrderedCommGroupWithZero.inl α β) a =
    (WithZero.map' ↑(toLexMulEquiv (αˣ × βˣ))) ((MonoidWithZeroHom.inl α β) a)

Defined in: Mathlib.Algebra.Order.GroupWithZero.Lex
Cited by: 2 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrderedCommGroupWithZero LinearOrderedCommGroupWithZero

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Unitsstatement · cited by 2,804
MulEquivstatement · cited by 1,142
MonoidWithZeroHomstatement · cited by 704
WithZerostatement · cited by 586
LinearOrderedCommGroupWithZerostatement and proof · cited by 528
Lexstatement · cited by 370
MonoidHomClass.toMonoidHomstatement · cited by 294
OrderMonoidWithZeroHomstatement · cited by 48
WithZero.map'statement · cited by 45
MonoidWithZeroHom.inlstatement · cited by 13
toLexMulEquivstatement · cited by 9

Cited by2

Results whose statement or proof uses this declaration.

LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗproof · cited by 1
LinearOrderedCommGroupWithZero.fst_comp_inlproof · cited by 0