Theorems · Definition · order theory
IsSimpleOrder.linearOrder
{α : Type u_2} →
[inst : PartialOrder α] → [inst_1 : BoundedOrder α] → [IsSimpleOrder α] → [DecidableEq α] → LinearOrder αA simple partial ordered BoundedOrder induces a linear order.
This is not an instance to prevent loops.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- LinearOrderstatement · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- Bot.botproof · cited by 4,720
- BoundedOrderstatement and proof · cited by 270
- IsSimpleOrderstatement and proof · cited by 54
- decidableLTOfDecidableLEproof · cited by 0
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