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Proof step 1 from proof rest-app (conclusion)

⊦ m ≤ # x + # y ∧ # x ≤ m → restn(m, x + y) = restn(m - # x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# x ≤ m, m ≤ # x + # y ⊦ restn(m, x + y) = restn(m - # x, y)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat