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Proof step 9 from proof putar-getar-01 (previous step)

0 < i0 + 1, 0 ≤ i0, ∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, st[r -- i '] ' + getarray(r, i + 1, i0, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = st[r -- i '] ' + getarray(r, i + 1, i0 + 1 - 1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ i0, ∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, getarray(r, i + 1, i0, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = getarray(r, i + 1, i0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ vals + vals0 = vals + vals1 ↔ vals0 = vals1], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0])]]