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Proof step 3 from proof papp-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
perm(x + y, x0 + y0), perm(x, x0), perm(x0, x), perm(x0 + y0, x + y) ⊦ perm(y, y0)

Rule argument

Additional information

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