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Proof step 1 from proof perm-del-01 (conclusion)

⊦ perm(x -l a, z) ∧ perm(x, y) → (¬ perm(y -l a, z) ↔ false)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
perm(x -l a, z), perm(x, y), perm(z, x -l a), perm(y, x) ⊦ perm(y -l a, z)

Rule argument

Additional information

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