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Proof step 57 from proof addarray-put-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
⊦ r ∈ addarray(r, ty0, i, st)
Proof step 56:
is_indexkey(sk), 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- sk ∈ addarray(r, ty, i0 + j + 1, st) ⊦ sk = _length, sk = _type, sk = j ', r -- sk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])]]