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Proof step 4 from proof shift-03 (previous step)

a ∈ y ⊦ perm(x + a ' + x0, y) ↔ perm(x + x0, y -1l a)

User applied rule structural induction

And obtained the following new goals

Proof step 5:
a ∈ y, ∀ a, y, x0. a ∈ y → (perm(x1 + a ' + x0, y) ↔ perm(x1 + x0, y -1l a)) ⊦ perm((a0 + x1) + a ' + x0, y) ↔ perm((a0 + x1) + x0, y -1l a)

Rule argument

indvar: x

Additional information

Used simplifier rules: del-01: ⊦ perm(a ' + x, y) ↔ a ∈ y ∧ perm(x, y -1l a);%list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list