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Proof step 1 from proof restn-at (conclusion)

⊦ m + n < # x → restn(m, x)[n] = x[m + n]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ m, n. m + n < # x0 → restn(m, x0)[n] = x0[m + n] ⊦ m + n < #(a + x0) → restn(m, a + x0)[n] = (a + x0)[m + n]

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%zero-01: ⊦ ¬ m < 0; from specification nat-basic1