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Proof step 1 from proof perm-com1 (conclusion)

⊦ perm(x + y, z) → perm(y + x, z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: neq: ⊦ perm(x, y) ∧ ¬ perm(x0, y) → x ≠ x0;%sym-01: ⊦ perm(x, y) → perm(y, x);%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%neq: ⊦ perm(x, y) ∧ ¬ perm(x0, y) → x ≠ x0;%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