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Proof step 52 from proof addarray-put-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ r ≠ r0 ∨ r = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) → (r0 -- sk ∈ addarray(r, ty, vals, st) ↔ r0 -- sk ∈ st)
Proof step 46:
¬ ( r ≠ r ∨ r = r ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# (mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)))) ≤ sk .index)), r -- sk ∈ addarray(r, ty, i0 + j + 1, st), is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 < j ⊦ sk = _length, sk = _type, sk = j ', j = 0, r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)
Proof step 51:
r ≠ r ∨ r = r ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# (mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)))) ≤ sk .index), r -- sk ∈ addarray(r, ty, i0 + j + 1, st), is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 < j ⊦ sk = _length, sk = _type, sk = j ', j = 0, r -- sk ∈ st

Rule argument

[crewrite-arg: add-in-other , F , [st, vals, ty, r, sk, r0] → [st, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), ty, r, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), ty, r, sk, r)]]