Mem elems No Exotics of no Exotics
FTheory.SU5.FluxesFive.mem_elemsNoExotics_of_noExotics
Project documentation
The allowed subsets of a FluxesFive which has no exotics or zeros. -/ def noExoticsSubsets : (n : ℕ) → Finset (Multiset Fluxes) | 0 => {{}} | 1 => {{⟨0, 1⟩}, {⟨0, 2⟩}, {⟨0, 3⟩}, {⟨1, -1⟩}, {⟨1, 0⟩}, {⟨1, 1⟩}, {⟨1, 2⟩}, {⟨2, -2⟩}, {⟨2, -1⟩}, {⟨2, 0⟩}, {⟨2, 1⟩}, {⟨3, -3⟩}, {⟨3, -2⟩}, {⟨3, -1⟩}, {⟨3, 0⟩}} | 2 => {{⟨0, 1⟩, ⟨0, 1⟩}, {⟨0, 1⟩, ⟨1, -1⟩}, {⟨0, 1...
Exact Lean statement
lemma mem_elemsNoExotics_of_noExotics (F : FluxesFive) (hNE : F.NoExotics) (hnZ : F.HasNoZero) :
F ∈ elemsNoExoticsFormal artifact
Lean source
lemma mem_elemsNoExotics_of_noExotics (F : FluxesFive) (hNE : F.NoExotics) (hnZ : F.HasNoZero) : F ∈ elemsNoExotics := by have h1 := card_mem_range_seven_of_noExotics hNE hnZ have hF := subset_of_fluxesFive_mem_noExoticsSubsets_of_noExotics hNE hnZ F (Preorder.le_refl F) simp only [Finset.range, Multiset.range_succ, Multiset.range_zero, Multiset.cons_zero, Finset.mk_cons, Finset.cons_eq_insert, Finset.mem_insert, Finset.mem_mk, Multiset.mem_singleton] at h1 rcases h1 with hr | hr | hr | hr | hr | hr | hr all_goals · rw [hr] at hF clear hr hnZ revert hNE revert F decide- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Fluxes/NoExotics/Completeness.lean:249-263
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