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Proof step 11 from proof insperm-01 (previous step)

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))

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: list-perm inst: name: trans seq: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z) subst: [x, y, z] → [ins≤(a, x), a ' + x, a ' + y] flags:

Additional information

Used simplifier rules: app: ⊦ perm(x + y, x + z) ↔ perm(y, z); from specification list-perm%a: ⊦ (x + y) + z = x + y + z; from specification list%trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z); (forward) from specification list-perm%sym-01: ⊦ perm(x, y) → perm(y, x); (forward) from specification list-perm Used terms: ins≤(a, x), a ' + x, a ' + y