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Proof step 3 from proof prefixn-shorter (previous step)

prefixn(n + 1, x0) = prefixn(n + 1, x1) ⊦ prefixn(n, x0) = prefixn(n, x1)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
prefixn(n + 1, []) = prefixn(n + 1, x1) ⊦ prefixn(n, []) = prefixn(n, x1)
Proof step 6:
prefixn(n + 1, a + x) = prefixn(n + 1, x1), ∀ n, x1. prefixn(n + 1, x) = prefixn(n + 1, x1) → prefixn(n, x) = prefixn(n, x1) ⊦ prefixn(n, a + x) = prefixn(n, x1)

Rule argument

indvar: x0

Additional information

Used simplifier rules: list freely generated by [], +;;