Right Metric Val expand tmul
Fermion.rightMetricVal_expand_tmul
Plain-language statement
Expansion of rightMetricVal into the left basis.
Exact Lean statement
lemma rightMetricVal_expand_tmul : rightMetricVal =
- RightHandedWeyl.basis 0 ⊗ₜ[ℂ] RightHandedWeyl.basis 1 +
RightHandedWeyl.basis 1 ⊗ₜ[ℂ] RightHandedWeyl.basis 0Formal artifact
Lean source
lemma rightMetricVal_expand_tmul : rightMetricVal = - RightHandedWeyl.basis 0 ⊗ₜ[ℂ] RightHandedWeyl.basis 1 + RightHandedWeyl.basis 1 ⊗ₜ[ℂ] RightHandedWeyl.basis 0 := by simp only [rightMetricVal, Fin.isValue] rw [rightRightToMatrix_symm_expand_tmul] simp only [metricRaw, Matrix.neg_apply, of_apply, cons_val', empty_val', cons_val_fin_one, Fin.sum_univ_two, Fin.isValue, cons_val_zero, cons_val_one, neg_zero, zero_smul, zero_add, neg_neg, one_smul, add_zero, add_left_inj] module- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Fermions/Weyl/Metric.lean:172-180
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