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Proof step 17 from proof putarray-addarray (previous step)

vals = vals1 + val0 ', n→i(# vals) + j = i0 + 1, 0 ≤ i, 0 ≤ j, i ≤ i0 + 1, j ≤ i, (~1) ≤ i0, ∀ st, val, r, j, i, vals0. # vals0 < # vals → ( 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j + n→i(# vals0) ∧ j ≤ i ∧ 0 ≤ j + n→i(# vals0) → putArray(vals0, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals0, 0, st)) ⊦ putArray(vals, r, j, addarray(r, val, i, st)) = (addarray(r, mklist(val, i→n(j)) + vals1, 0, st)[r -- i0 ', val0]), vals = [], mklist(val, i→n(j)) + vals = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
0 ≤ i, 0 ≤ j, i ≤ (n→i(# vals1) + j) + 1, j ≤ i, (~1) ≤ n→i(# vals1) + j, ∀ st, val, r, j, i, vals0. # vals0 < # (vals1 + val0 ') → ( 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j + n→i(# vals0) ∧ j ≤ i ∧ 0 ≤ j + n→i(# vals0) → putArray(vals0, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals0, 0, st)) ⊦ putArray(vals1 + val0 ', r, j, addarray(r, val, i, st)) = (addarray(r, mklist(val, i→n(j)) + vals1, 0, st)[r -- (n→i(# vals1) + j) ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : i < 0 ⊦ ((* i)) ≤ n→i(n)], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPSEQ : ⊦ vals + val ' ≠ []], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0])]]