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Proof step 32 from proof getarray-put=set (previous step)

1 < j, 0 ≤ i1, i1 < j, 0 < j, ∀ val, st, i, r, i1, j0. i→n(j0) < i→n(j) → (0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 → getarray(r, i, j0, st[r -- (i1 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i1), val])) ⊦ getarray(r, i, j - 1, st[r -- (i1 + i) ', val]) + (st[r -- (i1 + i) ', val][r -- (i + j - 1) ']) = (getarray(r, i, j, st)[i→n(i1), val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
0 ≤ i1, i1 < j, 1 < j, 0 < j, ∀ val, st, i, r, i1, j0. i→n(j0) < i→n(j) → (0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 → getarray(r, i, j0, st[r -- (i1 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i1), val])) ⊦ getarray(r, i, j - 1, st[r -- (i1 + i) ', val]) + ((j = i1 + 1 ⊃ val; st[r -- (i + j - 1) '])) ' = (getarray(r, i, j, st)[i→n(i1), val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j], [CSIMPSEQ : ⊦ vals + val = vals + val '], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))])]]