Theorems · Theorem · order theory
RelSeries.step
∀ {α : Type u_1} {r : SetRel α α} (self : RelSeries r) (i : Fin self.length),
(self.toFun i.castSucc, self.toFun i.succ) ∈ rAdjacent elements are related
- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetRelstatement and proof · cited by 581
- RelSeries.lengthstatement · cited by 195
- RelSeriesstatement and proof · cited by 129
- RelSeries.toFunstatement · cited by 114
Cited by18
Results whose statement or proof uses this declaration.
- Order.length_le_heightproof · cited by 5
- RelSeries.eraseLast_last_rel_lastproof · cited by 4
- CompositionSeries.isMaximal_eraseLast_lastproof · cited by 3
- RelSeries.rel_of_ltproof · cited by 3
- isFiniteLength_of_exists_compositionSeriesproof · cited by 3
- Order.height_coe_withTopproof · cited by 3
- RelSeries.length_ne_zeroproof · cited by 2
- Order.height_le_of_krullDim_preimage_leproof · cited by 2
- CompositionSeries.lt_succproof · cited by 1
- LTSeries.apply_add_index_le_apply_add_index_intproof · cited by 1
- LTSeries.apply_add_index_le_apply_add_index_natproof · cited by 1
- IsLocalRing.length_restrictScalarsproof · cited by 1