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Proof step 6 from proof add-put-switch (previous step)

is_fskey(sk), 0 ≤ i1, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i1 + 1) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i1, st[r0 -- sk, val0])[r0 -- i1 ', val]) = (addarray(r0, val, i1, st)[r0 -- sk, val0][r0 -- i1 ', val]), sk = i1 '

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [val0, st, val, r0, sk, i0] → [val0, st, val, r0, sk, i1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (val0, st, val, r0, sk, i1)]]