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Proof step 4 from proof appins (previous step)

⊦ sort(x + ins≤(a, y)) = ins≤(a, sort(x + y)), perm(x + ins≤(a, y), a ' + sort(x + y)), perm(x + ins≤(a, y), ins≤(a, sort(x + y))), perm(a ' + sort(x + y), x + ins≤(a, y))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ perm(a ' + x, y) ↔ a ∈ y ∧ perm(x, y -1l a)
Proof step 6:
⊦ sort(x + ins≤(a, y)) = ins≤(a, sort(x + y)), perm(x + ins≤(a, y), a ' + sort(x + y)), perm(x + ins≤(a, y), ins≤(a, sort(x + y))), a ∈ x + ins≤(a, y) ∧ perm(sort(x + y), (x + ins≤(a, y)) -1l a)

Rule argument

spec: list-perm inst: name: perm-l seq: ⊦ perm(a ' + x, y) ↔ a ∈ y ∧ perm(x, y -1l a) subst: [y, x, a] → [x + ins≤(a, y), sort(x + y), a] flags: rewrite

Additional information

Used terms: x + ins≤(a, y), sort(x + y), a