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Proof step 15 from proof shift-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
perm(x + a ' + x0, y), perm(y, x + a ' + x0) ⊦ a ∈ y

Rule argument

Additional information

Used simplifier rules: sym-01: ⊦ perm(x, y) → perm(y, x);%trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z);%perm-rmv-in-list: ⊦ perm(x + a ' + y, x0 + a ' + y0) ↔ perm(x + y, x0 + y0);%app: ⊦ perm(x + y, x + z) ↔ perm(y, z);%ref: ⊦ perm(x, x);%a: ⊦ (x + y) + z = x + y + z; from specification list