diff options
Diffstat (limited to 'Nominal/Instances/Basic.lean')
| -rw-r--r-- | Nominal/Instances/Basic.lean | 5 |
1 files changed, 5 insertions, 0 deletions
diff --git a/Nominal/Instances/Basic.lean b/Nominal/Instances/Basic.lean index d41e87f..dea5bcf 100644 --- a/Nominal/Instances/Basic.lean +++ b/Nominal/Instances/Basic.lean @@ -282,6 +282,11 @@ lemma supp {x : X} : NominalSet.supp 𝔸 (Quotient.mk setoid.toSetoid x) = {a | simp only [FPerm.swap_inv, PermSet.atom_swap, Equiv.swap_apply_left] exact hc.right +/-- If an atom is not in the support of the equivalence class, one can always pick a representative where it is not in the least support. -/ +lemma supp_pick_fresh {a : 𝔸} {x : X} : a ∉ NominalSet.supp 𝔸 (Quotient.mk setoid.toSetoid x) → ∃ (y : X), y ≈ x ∧ a ∉ NominalSet.supp 𝔸 y := by + contrapose + simp [not_exists, not_and, not_not, supp] + end Quotient end Quotient |