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Proof step 169 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 ']), ¬ i0 < 0 ∧ ¬ i + n→i(# vals) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 157:
⊦ i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i ']
Proof step 168:
i0 < i ∨ n→i(# vals) + i ≤ i0, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (addarray(r, ty, j, st)[r -- i0 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 ']), ¬ i0 < 0 ∧ ¬ i + n→i(# vals) ≤ i0

Rule argument

[speclemmaarg: , i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i '] ,[i, r0, st, j, r, vals] → [i0, r, addarray(r, ty, j, st), i, r, vals] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j ∧ j < i + n→i(# vals) → (putArray(vals, r, i, st) [r -- j ' ] ) = vals[i→n(j - i)]], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i0, r, addarray(r, ty, j, st), i, r, vals)]]