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Proof step 14 from proof putarray-addarray (previous step)

0 ≤ j + n→i(# vals1) ∧ 0 ≤ j ∧ j + n→i(# vals1) ≤ j + n→i(# vals1), 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, r, j, addarray(r, val, i, st))[r -- (j + n→i(# vals1)) ', val0]) = (addarray(r, mklist(val, i→n(j)) + vals1, 0, st)[r -- (n→i(# vals1) + j) ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 ≤ i, 0 ≤ j, i ≤ (n→i(# vals1) + j) + 1, j ≤ i, 0 ≤ j + n→i(# vals1), ∀ 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, r, j, addarray(r, val, i, st))[r -- (j + n→i(# vals1)) ', val0]) = (addarray(r, mklist(val, i→n(j)) + vals1, 0, st)[r -- (n→i(# vals1) + j) ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ i + j = j + i])]]