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Proof step 7 from proof insperm-02 (previous step)

a0 < a, ∀ a, y. perm(ins≤(a, x0 + y), ins≤(a, x0) + y) ⊦ perm(ins≤(a, a0 ' + x0) + y, ins≤(a, (a0 ' + x0) + y)), perm(ins≤(a, (a0 ' + x0) + y), ins≤(a, a0 ' + x0) + y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
a0 < a, ∀ a, y. perm(ins≤(a, x0 + y), ins≤(a, x0) + y) ⊦ perm(ins≤(a, x0) + y, ins≤(a, x0 + y)), perm(ins≤(a, x0 + y), ins≤(a, x0) + y)

Rule argument

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x); (forward) from specification list-perm%app: ⊦ perm(x + y, x + z) ↔ perm(y, z); from specification list-perm%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list