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Proof step 68 from proof addarray-put-01 (previous step)

0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ r ≠ r0 ∨ r = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ j ≤ sk .index) → (r0 -- sk ∈ addarray(r, ty, j, st) ↔ r0 -- sk ∈ st)
Proof step 66:
¬ (r ≠ r ∨ r = r ∧ is_fskey(i ') ∧ i ' ≠ _length ∧ i ' ≠ _type ∨ r = r ∧ is_indexkey(i ') ∧ (i ' .index < 0 ∨ 1 + i0 ≤ i ' .index)), 0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)
Proof step 67:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)

Rule argument

[crewrite-arg: in-1dim-other , F , [st, j, ty, r, sk, r0] → [st, 1 + i0, ty, r, i ', r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ i ' .index = i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (st, 1 + i0, ty, r, i ', r)]]