Succ Succ Above comm
TensorSpecies.Tensor.IsReindexing.succSuccAbove_comm
Plain-language statement
Removing two pairs of entries from c in either order gives the same colour list: removing the i1-th and j1-th entries and then the (shifted) i2-th and j2-th entries matches removing the i2-th and j2-th entries first and then the (shifted) i1-th and j1-th entries, via the identity permutation. This is used for the commutation of two *cont...
Exact Lean statement
lemma succSuccAbove_comm {n : ℕ} {c : Fin (n + 1 + 1 + 1 + 1) → C}
(i1 j1 : Fin (n + 1 + 1 + 1 + 1)) (i2 j2 : Fin (n + 1 + 1))
(hij1 : i1 ≠ j1) (hij2 : i2 ≠ j2) :
let i2'Formal artifact
Lean source
lemma succSuccAbove_comm {n : ℕ} {c : Fin (n + 1 + 1 + 1 + 1) → C} (i1 j1 : Fin (n + 1 + 1 + 1 + 1)) (i2 j2 : Fin (n + 1 + 1)) (hij1 : i1 ≠ j1) (hij2 : i2 ≠ j2) : let i2' := (i1.succSuccAbove j1 i2); let j2' := (i1.succSuccAbove j1 j2); have hi2j2' : i2' ≠ j2' := by simp [i2', j2', hij2]; let i1' := (predPredAbove i2' j2' hi2j2' i1 (by simp [i2', j2'])); let j1' := (predPredAbove i2' j2' hi2j2' j1 (by simp [i2', j2'])); IsReindexing ((c ∘ i2'.succSuccAbove j2') ∘ i1'.succSuccAbove j1') ((c ∘ i1.succSuccAbove j1) ∘ i2.succSuccAbove j2) id := by apply And.intro (Function.bijective_id) simp only [id_eq, Function.comp_apply] intro i rw [succSuccAbove_comm_apply] · simp [hij1] · simp [hij2]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Reindexing.lean:388-403
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