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Proof step 79 from proof addarray-put-01 (previous step)

0 < j, 0 ≤ i0, 0 ≤ i0 + j, i ≤ j + i0, 0 ≤ i ⊦ j = 0, i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ 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 78:
¬ (r ≠ r ∨ r = r ∧ is_fskey(i ') ∧ i ' ≠ _length ∧ i ' ≠ _type ∨ r = r ∧ is_indexkey(i ') ∧ (i ' .index < 0 ∨ i0 + j + 1 ≤ i ' .index)), 0 < j, 0 ≤ i0, 0 ≤ i0 + j, i ≤ j + i0, 0 ≤ i ⊦ j = 0, i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(i ')], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ i ' .index = i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRATERMS : (st, i0 + j + 1, ty, r, i ', r)]]