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Proof step 4 from proof papp-02 (previous step)

perm(x, x0), perm(x + y, y0 + x0), perm(x0, x), perm(x0 + y0, x + y) ⊦ perm(y, y0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
perm(x0 + y0, x + y), perm(x, x0), perm(x + y, y0 + x0), perm(x0, x), perm(x + y, x0 + y0) ⊦ perm(y, y0)

Rule argument

Additional information

Used simplifier rules: trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z);%sym-01: ⊦ perm(x, y) → perm(y, x);%app-02: ⊦ perm(x + y, z + x) ↔ perm(y, z);%ref: ⊦ perm(x, x);%app: ⊦ perm(x + y, x + z) ↔ perm(y, z);%a: ⊦ (x + y) + z = x + y + z; from specification list