Theorems · Theorem · order theory
min_le_min
∀ {α : Type u} [inst : LinearOrder α] {a b c d : α}, c ≤ a → d ≤ b → min c d ≤ min a b- Defined in
- Mathlib.Order.MinMax
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- inf_le_infproof · cited by 54
Cited by11
Results whose statement or proof uses this declaration.
- Set.monotone_projIccproof · cited by 4
- IsMinFilter.minproof · cited by 3
- IsMaxFilter.minproof · cited by 3
- HasFPowerSeriesWithinOnBall.prodproof · cited by 2
- CauSeq.lt_infproof · cited by 1
- MeasureTheory.Submartingale.stoppedProcessproof · cited by 1
- CauSeq.sup_ltproof · cited by 1
- EisensteinSeries.r_lower_bound_on_verticalStripproof · cited by 1
- MeasureTheory.hittingBtwn_le_iff_of_existsproof · cited by 1
- Set.monotone_projIicproof · cited by 1
- Set.OrdConnected.IicExtendproof · cited by 0