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Proof step 2 from proof from-rest (previous step)

a ∈ x ⊦ frome(x, a) = restn(pos(a, x), x)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a. a ∈ x0 → frome(x0, a) = restn(pos(a, x0), x0), a ∈ a0 + x0 ⊦ frome(a0 + x0, a) = restn(pos(a, a0 + x0), a0 + x0)

Rule argument

term: x

Additional information

Used simplifier rules: fromE-empty: ⊦ frome([], a) = [];%pos-e: ⊦ pos(a, []) = 0;%restN-zero: ⊦ restn(0, x) = x;%list freely generated by [], +;;