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Proof step 30 from proof getarray-put=set (previous step)

j = i0 + 1, 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, i0, st[r -- (i1 + i) ', val]) + ((j = i1 + 1 ⊃ val; st[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 29:
0 ≤ i1, i1 ≤ i0, 0 ≤ i0, 0 < i0, ∀ val, st, i, r, i1, j0. i→n(j0) < i→n(i0 + 1) → (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, i0, st[r -- (i1 + i) ', val]) + ((i0 = i1 ⊃ val; st[r -- (i + i0) '])) ' = (getarray(r, i, i0 + 1, st)[i→n(i1), val])

Rule argument

[emptyarg]

Additional information

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