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Proof step 25 from proof getarray-put=set (previous step)

0 ≤ i0, 0 ≤ i1, i1 < 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])) ⊦ i0 = i1, getarray(r, i, i0, st[r -- (i1 + i) ', val]) + st[r -- (i + i0) '] ' = (getarray(r, i, i0, st) + st[r -- (i + i0) '] ')[i→n(i1), val]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ n < # vals → (vals + val ')[n, val0] = vals[n, val0] + val '
Proof step 20:
⊦ 0 < j → # getarray(r, i, j, st) = i→n(j)
Proof step 24:
i→n(i1) < # getarray(r, i, i0, st), 0 ≤ i0, 0 ≤ i1, i1 < 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])) ⊦ i0 = i1, getarray(r, i, i0, st[r -- (i1 + i) ', val]) + st[r -- (i + i0) '] ' = (getarray(r, i, i0, st)[i→n(i1), val]) + st[r -- (i + i0) '] '

Rule argument

[speclemmaarg: ,n < # vals → (vals + val ')[n, val0] = vals[n, val0] + val ' ,[val0, n, val, vals] → [val, i→n(i1), st[r -- (i + i0) '], getarray(r, i, i0, st)] ,F ,list-del ,javavalues ,put-butlast ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ 0 < j → abs(j) = j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i < j → ¬ j < i])], [EXTRATERMS : (val, i→n(i1), st[r -- (i + i0) '], getarray(r, i, i0, st))]]