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Proof step 13 from proof addarray-is-putarray (previous step)

i = i1 + 1, 0 ≤ i, 0 < i, ∀ st, val, r, i0. i→n(i0) < i→n(i) → (0 ≤ i0 → addarray(r, val, i0, st) = putArray(mklist(val, i→n(i0)), r, 0, st)) ⊦ (addarray(r, val, i1, st)[r -- i1 ', val]) = putArray(mklist(val, i→n(i)), r, 0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → addarray(r, val, i0, st) = putArray(mklist(val, i→n(i0)), r, 0, st)) ⊦ (addarray(r, val, i1, st)[r -- i1 ', val]) = putArray(mklist(val, i→n(i1) + 1), r, 0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ 0 < i + 1 → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]