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Proof step 8 from proof insperm-01 (previous step)

perm(x, y), perm(a ' + y, ins≤(a, y)), perm(a ' + x, ins≤(a, x)), perm(ins≤(a, x), a ' + x), perm(ins≤(a, y), a ' + y) ⊦ perm(ins≤(a, x), ins≤(a, y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
perm(x, y), perm(a ' + y, ins≤(a, y)), perm(a ' + x, ins≤(a, x)), perm(ins≤(a, x), a ' + x), perm(ins≤(a, y), a ' + y), perm(y, x) ⊦ perm(ins≤(a, x), ins≤(a, y)), perm(ins≤(a, y), ins≤(a, x))

Rule argument

Additional information

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