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Proof step 210 from proof putarray-addarray-01 (previous step)

is_fskey(sk), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _type, sk = _length, ( r -- sk ∈ addarray(r, ty, j, st) ∨ (r -- sk) .ref = r ∧ is_indexkey((r -- sk) .key) ∧ i ≤ (r -- sk) .key .index ∧ (r -- sk) .key .index < i + n→i(# vals) → r -- sk ∈ st) ∧ st[r -- sk] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 206:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 209:
is_fskey(sk), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _type, sk = _length, (is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) → r -- sk ∈ st) ∧ st[r -- sk] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .key = sk], [CSIMPSEQ : ⊦ (r -- sk) .ref = r])]]