Uncontracted List succ Above Emb erase Idx to Finset
WickContraction.uncontractedList_succAboveEmb_eraseIdx_toFinset
Project documentation
The embedding of Fin [φsΛ]ᵘᶜ.length into Fin φs.length. -/ def uncontractedListEmd {φs : List 𝓕.FieldOp} {φsΛ : WickContraction φs.length} : Fin [φsΛ]ᵘᶜ.length ↪ Fin φs.length := ((finCongr (by simp [uncontractedListGet])).trans φsΛ.uncontractedIndexEquiv).toEmbedding.trans (Function.Embedding.subtype fun x => x ∈ φsΛ.uncontracted) lemma uncontracted...
Exact Lean statement
lemma uncontractedList_succAboveEmb_eraseIdx_toFinset (c : WickContraction n) (i : Fin n.succ)
(k : ℕ) (hk : k < c.uncontractedList.length) :
((List.map i.succAboveEmb c.uncontractedList).eraseIdx k).toFinset =
(c.uncontracted.map i.succAboveEmb).erase (i.succAboveEmb c.uncontractedList[k])Formal artifact
Lean source
lemma uncontractedList_succAboveEmb_eraseIdx_toFinset (c : WickContraction n) (i : Fin n.succ) (k : ℕ) (hk : k < c.uncontractedList.length) : ((List.map i.succAboveEmb c.uncontractedList).eraseIdx k).toFinset = (c.uncontracted.map i.succAboveEmb).erase (i.succAboveEmb c.uncontractedList[k]) := by ext a simp only [Fin.coe_succAboveEmb, List.mem_toFinset, Fin.succAboveEmb_apply, Finset.mem_erase, ne_eq, Finset.mem_map] rw [mem_eraseIdx_nodup _ _ _ (by simpa using hk)] · simp only [List.mem_map, List.getElem_map, ne_eq, uncontractedList_mem_iff] tauto · exact uncontractedList_succAboveEmb_nodup c i- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QFT/PerturbationTheory/WickContraction/UncontractedList.lean:457-467
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