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Proof step 5 from proof shift-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a ∈ y, ∀ a, y, x0. a ∈ y → (perm(x1 + a ' + x0, y) ↔ perm(x1 + x0, y -1l a)) ⊦ a0 ∈ y ∧ perm(x1 + a ' + x0, y -1l a0) ↔ a0 ∈ y -1l a ∧ perm(x1 + x0, (y -1l a) -1l a0)

Rule argument

Additional information

Used simplifier rules: del-01: ⊦ perm(a ' + x, y) ↔ ¬ ¬(a ∈ y ∧ perm(x, y -1l a));%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list