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Theorems · Theorem · order theory

GradeMinOrder.isMin_grade

∀ {𝕆 : Type u_5} {α : Type u_6} {inst : Preorder 𝕆} {inst_1 : Preorder α} [self : GradeMinOrder 𝕆 α] ⦃a : α⦄,
  IsMin a → IsMin (GradeOrder.grade a)

Minimal elements have minimal grades.

Defined in
Mathlib.Order.Grade
Cited by
1 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
GradeMinOrder
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Around this declaration

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

IsMin.grade · cited by 2IsMin.gradePreorder · cited by 7952PreorderIsMin · cited by 277IsMinGradeOrder.grade · cited by 5GradeOrder.gradeGradeMinOrder · cited by 5GradeMinOrderGradeMinOrder.isMin_gradeCITED BYCITES

Cites4

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Cited by1

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