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Proof step 97 from proof addarray-put-01 (previous step)

0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, is_indexkey(sk) ⊦ sk = j ', r -- sk ∈ addarray(r, ty, i0 + j + 1, st) ↔ r -- sk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), sk = _type, sk = _length

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 95:
¬ (is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type), 0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j, is_indexkey(sk) ⊦ sk = j ', r -- sk ∈ addarray(r, ty, i0 + j + 1, st) ↔ r -- sk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), sk = _type, sk = _length
Proof step 96:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, vals, st) ↔ r -- sk ∈ st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0 + j + 1, ty, sk, r)]]