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Proof step 6 from proof insperm-02 (previous step)

∀ 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 weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
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)

Rule argument

fma: a0 < a

Additional information

Used simplifier rules: ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%app: ⊦ perm(x + y, x + z) ↔ perm(y, z); from specification list-perm%ref: ⊦ perm(x, x); from specification list-perm Used formulas: a0 < a