Theorems · Theorem · combinatorics
Fin.insertNth_apply_succAbove
∀ {n : ℕ} {α : Fin (n + 1) → Sort u_1} (i : Fin (n + 1)) (x : α i) (p : (j : Fin n) → α (i.succAbove j)) (j : Fin n),
i.insertNth x p (i.succAbove j) = p j- Defined in
- Mathlib.Data.Fin.Tuple.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fin.succAbovestatement and proof · cited by 249
- Fin.insertNthstatement · cited by 95
- Fin.castPredproof · cited by 89
- Fin.ne_zero_of_ltproof · cited by 32
- Fin.ne_last_of_ltproof · cited by 25
- Fin.succAbove_neproof · cited by 8
- Fin.succAbove_castPred_of_ltproof · cited by 5
- Fin.succAbove_lt_iff_castSucc_ltproof · cited by 3
- Fin.lt_succAbove_iff_le_castSuccproof · cited by 3
- Fin.castPred_succAboveproof · cited by 1
- Fin.pred_succAboveproof · cited by 1
Cited by23
Results whose statement or proof uses this declaration.
- Fin.insertNth_eq_iffproof · cited by 6
- Fin.removeNth_insertNthproof · cited by 5
- Fin.insertNth_binopproof · cited by 4
- finSuccEquiv'_succAboveproof · cited by 4
- MeasureTheory.measurePreserving_piFinSuccAboveproof · cited by 3
- Fin.insertNth_injective2proof · cited by 3
- Fin.insertNth_revproof · cited by 3
- Filter.Tendsto.finInsertNthproof · cited by 2
- Fin.insertNth_apply_cycleRange_symmproof · cited by 2
- Fin.nndist_insertNth_insertNthproof · cited by 1
- Finset.map_insertNthEquiv_filter_piFinsetproof · cited by 1