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Proof step 4 from proof put-app-right (previous step)

⊦ (x + y)[n0 + # x, a] = x + y[n0, a]

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ y, n0, a. (x0 + y)[n0 + # x0, a] = x0 + y[n0, a] ⊦ ((a0 + x0) + y)[n0 + #(a0 + x0), a] = (a0 + x0) + y[n0, a]

Rule argument

term: x

Additional information

Used simplifier rules: list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2