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Theorems · Theorem · order theory

WithBot.pred_coe_of_not_isMin

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : PredOrder α] [inst_2 : (a : α) → Decidable (Order.pred a = a)]
  {a : α}, ¬IsMin a → Order.pred ↑a = ↑(Order.pred a)
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
PartialOrderPredOrderDecidable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithBot.pred_coe · cited by 0WithBot.pred_coePartialOrder · cited by 6410PartialOrderWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someIff.not · cited by 489Iff.notPredOrder · cited by 334PredOrderIsMin · cited by 277IsMinOrder.pred · cited by 273Order.predOrder.pred_eq_iff_isMin · cited by 8Order.pred_eq_iff_isMinWithBot.pred_coe_of_not_isMinCITED BYCITES

Cites8

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Cited by1

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