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Proof step 81 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 74:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 80:
¬ (is_fskey(i ') ∧ i ' ≠ _length ∧ i ' ≠ _type), 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-fskey , F , [st, i, ty, sk, r] → [st, i0 + j + 1, ty, i ', r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')])], [EXTRATERMS : (st, i0 + j + 1, ty, i ', r)]]