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Proof step 2 from proof restN-append (previous step)

n ≤ # x ⊦ restn(n, x + y) = restn(n, x) + y

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ x, y. n0 ≤ # x → restn(n0, x + y) = restn(n0, x) + y, n0 +1 ≤ # x ⊦ restn(n0 +1, x + y) = restn(n0 +1, x) + y

Rule argument

indvar: n

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;%nat freely generated by 0, +1;;%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list