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Proof step 102 from proof putarray-addarray-01 (previous step)

is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ sk = _length, (r -- sk ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) ↔ r -- sk ∈ st) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- sk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 98:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 99:
⊦ is_fskey(sk) ∧ sk ≠ _type ∧ sk ≠ _length → (addarray(r, ty, i, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 101:
is_fskey(sk), 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ 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 + mklist(initial_value(ty), i→n(i0)), st)[r -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(sk) → (putArray(vals, r, i, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ i + j = j + i])]]