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Theorems · Theorem · order theory

zero_max

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : Zero α] [IsBotZeroClass α] (a : α), max 0 a = a
Defined in
Mathlib.Algebra.Order.IsBotOne
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
LinearOrderZeroIsBotZeroClass
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Around this declaration

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

Ordinal.max_zero_left · cited by 0Ordinal.max_zero_leftLinearOrder · cited by 8572LinearOrderzero_le · cited by 382zero_lesup_of_le_right · cited by 143sup_of_le_rightIsBotZeroClass · cited by 71IsBotZeroClasszero_maxCITED BYCITES

Cites4

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

Cited by1

Results whose statement or proof uses this declaration.