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Proof step 190 from proof addarray-put-01 (previous step)

¬ (is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type), 0 ≤ i0, 0 ≤ i0 + j, 0 < j ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j ', j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 144:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)
Proof step 145:
⊦ (addarray(r, ty, vals, st)[r -- _length]) = intval(n→i(# vals))
Proof step 146:
⊦ (addarray(r, ty, i, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 147:
⊦ (addarray(r, ty, vals, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 189:
0 ≤ i0, 0 ≤ i0 + j, 0 < j, is_indexkey(sk) ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j ', j = 0, sk = _type, sk = _length

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0], [CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]