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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ perm(a ' + x, a ' + y) ↔ perm(x, y)
Proof step 11:
perm(a ' + x, a ' + 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

spec: list-perm inst: name: cons seq: ⊦ perm(a ' + x, a ' + y) ↔ perm(x, y) subst: [a, x, y] → [a, x, y] flags: rewrite

Additional information

Used terms: a, x, y