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Proof step 3 from proof perm-mklist-del (previous step)

∀ x, a. (perm(x, mklist(a, #oc(a, x)) + y0) ↔ perm(x -l a, y0)) ∨ a ∈ y0 ⊦ perm(x, mklist(a, #oc(a, x)) + (a0 + y0)) ↔ perm(x -l a, a0 + y0), a ∈ a0 + y0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ x, a. (perm(x, mklist(a, #oc(a, x)) + y0) ↔ perm(x -l a, y0)) ∨ a ∈ y0 ⊦ a = a0, perm(x, mklist(a, #oc(a, x)) + a0 ' + y0) ↔ a0 ∈ x ∧ perm((x -l a) -1l a0, y0), a ∈ y0

Rule argument

Additional information

Used simplifier rules: del-03: ⊦ perm(x, a ' + y) ↔ ¬ ¬(a ∈ x ∧ perm(x -1l a, y));%in-del-new: ⊦ a ∈ x -l b ↔ a ∈ x ∧ a ≠ b; from specification list-del%in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list