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Theorems · Theorem · order theory

Order.not_isMax_zero

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : Zero α] [inst_2 : One α] [ZeroLEOneClass α] [NeZero 1], ¬IsMax 0
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderZeroOneZeroLEOneClassNeZero
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Around this declaration

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

Order.one_le_iff_pos · cited by 27Order.one_le_iff_posOrder.lt_one_iff_nonpos · cited by 2Order.lt_one_iff_nonposPartialOrder · cited by 6410PartialOrderIsMax · cited by 372IsMaxZeroLEOneClass · cited by 304ZeroLEOneClassone_pos · cited by 102one_posnot_isMax_iff · cited by 24not_isMax_iffOrder.not_isMax_zeroCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.