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Proof step 5 from proof perm-last-rec (previous step)

∀ x, a. perm(x, y0 + a ') ↔ a ∈ x ∧ perm(x -1l a, y0) ⊦ perm(x, (a0 + y0) + a ') ↔ a ∈ x ∧ perm(x -1l a, a0 + y0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ x, a. perm(x, y0 + a ') ↔ a ∈ x ∧ perm(x -1l a, y0) ⊦ a0 ∈ x ∧ perm(x -1l a0, y0 + a ') ↔ a ∈ x ∧ a0 ∈ x -1l a ∧ perm((x -1l a) -1l a0, y0)

Rule argument

Additional information

Used simplifier rules: del-03: ⊦ perm(x, a ' + y) ↔ ¬ ¬(a ∈ x ∧ perm(x -1l a, y));%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list