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Theorems · Theorem · order theory

SemilatticeInf.inf_le_left

∀ {α : Type u} [self : SemilatticeInf α] (a b : α), SemilatticeInf.inf a b ≤ a

The infimum is a lower bound on the first argument

Defined in
Mathlib.Order.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
SemilatticeInf
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Around this declaration

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

inf_le_left · cited by 286inf_le_leftDividedPowers.isSubDPIdeal_inf_iff · cited by 2DividedPowers.isSubDPIdea…GaloisCoinsertion.liftLattice · cited by 0GaloisCoinsertion.liftLat…Function.Injective.lattice · cited by 0Injective.latticeGaloisInsertion.liftLattice · cited by 0GaloisInsertion.liftLatti…Lattice.ofIsLUBofIsGLB · cited by 0Lattice.ofIsLUBofIsGLBSemilatticeInf · cited by 634SemilatticeInfSemilatticeInf.inf · cited by 3SemilatticeInf.infSemilatticeInf.inf_le_leftCITED BYCITES

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Cited by6

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