Theorems · Inductive type · order theory
GradeOrder
(𝕆 : Type u_5) → (α : Type u_6) → [Preorder 𝕆] → [Preorder α] → Type (max u_5 u_6)
An 𝕆-graded order is an order α equipped with a strictly monotone function
grade 𝕆 : α → 𝕆 which preserves order covering (CovBy).
- Defined in
- Mathlib.Order.Grade
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
Cited by42
Results whose statement or proof uses this declaration.
- gradestatement and proof · cited by 24
- grade_strictMonostatement and proof · cited by 7
- GradeOrder.gradestatement and proof · cited by 5
- GradeOrder.grade_strictMonostatement and proof · cited by 3
- grade_injectivestatement and proof · cited by 2
- CovBy.gradestatement and proof · cited by 2
- grade_lt_grade_iffstatement and proof · cited by 1
- GradeOrder.covBy_gradestatement and proof · cited by 1
- covBy_iff_lt_covBy_gradestatement and proof · cited by 1
- GradeMaxOrder.casesOnstatement and proof · cited by 0
- GradeMaxOrder.liftLeftproof · cited by 0
- GradeMaxOrder.liftRightproof · cited by 0