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Theorems · Theorem · order theory

Nat.sInf_le

∀ {s : Set ℕ} {m : ℕ}, m ∈ s → sInf s ≤ m
Defined in
Mathlib.Order.Lattice.Nat
Cited by
20 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.dist_le · cited by 5SimpleGraph.dist_leDirichletCharacter.conductor_one · cited by 3DirichletCharacter.conduc…Int.absNorm_under_eq_sInf · cited by 2Int.absNorm_under_eq_sInfMeasureTheory.Measure.haar.index_union_le · cited by 2haar.index_union_leMeasureTheory.Measure.haar.addIndex_union_le · cited by 2haar.addIndex_union_leDirichletCharacter.conductor_dvd_of_mem_conductorSet · cited by 2DirichletCharacter.conduc…Module.End.maxUnifEigenspaceIndex_le_finrank · cited by 1End.maxUnifEigenspaceInde…Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_one · cited by 1AbsoluteValue.exists_mini…Nat.eq_Ici_of_nonempty_of_upward_closed · cited by 1Nat.eq_Ici_of_nonempty_of…gaussSum_eq_zero_of_isPrimitive_of_not_isPrimitive · cited by 1gaussSum_eq_zero_of_isPri…MeasureTheory.Measure.haar.index_mono · cited by 1haar.index_monoMeasureTheory.Measure.haar.index_union_eq · cited by 1haar.index_union_eqMeasureTheory.Measure.haar.le_addIndex_mul · cited by 1haar.le_addIndex_mulMeasureTheory.Measure.haar.le_index_mul · cited by 1haar.le_index_mulMeasureTheory.Measure.haar.mul_left_index_le · cited by 1haar.mul_left_index_leSet · cited by 53352SetInfSet.sInf · cited by 935InfSet.sInfNat.find_min' · cited by 28Nat.find_min'Nat.sInf_def · cited by 13Nat.sInf_defNat.sInf_leCITED BYCITES

Cites4

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Cited by20

Results whose statement or proof uses this declaration.