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Proof step 31 from proof getarray-put=set (previous step)

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])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
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])

Rule argument

[speclemmaarg: ,i0 = i - j ↔ i = i0 + j ,[i, j, i0] → [j, 1, i0] ,T ,int-abs , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ i0 = i - j ↔ i = i0 + j])], [EXTRATERMS : (j, 1, i0)]]