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Proof step 1 from proof perm-shift-in2 (conclusion)

⊦ perm(x, y + z + a ') → perm(x, y + a ' + z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
perm(x -1l a, y + z), a ∈ x, perm(y + z, x -1l a) ⊦ perm(x, y + a ' + z)

Rule argument

Additional information

Used simplifier rules: perm-last-rec: ⊦ perm(x, y + a ') ↔ a ∈ x ∧ perm(x -1l a, y);%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);%ref: ⊦ perm(x, x);%app: ⊦ perm(x + y, x + z) ↔ perm(y, z);%a: ⊦ (x + y) + z = x + y + z; from specification list