Theorems · Theorem · order theory
OrderIso.sumLexIicIoi_apply_inl
∀ {α : Type u_1} [inst : LinearOrder α] {x : α} (a : ↑(Set.Iic x)), (OrderIso.sumLexIicIoi x) (toLex (Sum.inl a)) = ↑a- Defined in
- Mathlib.Order.Hom.Lex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Set.Ioistatement · cited by 1,463
- Set.Iicstatement and proof · cited by 1,111
- OrderIsostatement · cited by 874
- Lexstatement · cited by 370
- toLexstatement · cited by 195
- OrderIso.sumLexIicIoistatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- OrderIso.sumLexIicIoi_symm_apply_of_leproof · cited by 1