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Proof step 12 from proof putarray-addarray (previous step)

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)) ⊦ 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j + n→i(# vals1) ∧ j ≤ i ∧ 0 ≤ j + n→i(# vals1), (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 7:
⊦ 0 ≤ i → addarray(r, val, i + 1, st) = (addarray(r, val, i, st)[r -- i ', val])
Proof step 11:
0 ≤ j, 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, n→i(# vals1) + j, st)[r -- (n→i(# vals1) + j) ', val])[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 : ([CSIMPSEQ : ⊦ m ≤ m], [CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i = (j + n→i(n)) + 1 → j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]