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Proof step 200 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk]), sk = _length, ¬ is_indexkey(sk) ∧ sk ≠ _type

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 152:
⊦ (addarray(r, ty, i, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 153:
⊦ (addarray(r, ty, vals, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 199:
0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, is_indexkey(sk) ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk]), sk = _length, sk = _type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0], [CSIMPSEQ : ⊦ (putArray(vals, r, i, st) [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPSEQ : ⊦ _type ≠ _length])]]