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Proof step 33 from proof addarray-put-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 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)

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