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Proof step 65 from proof putarray-addarray-01 (previous step)

0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- i1 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- i1 ']), ¬ i1 < i ∧ ¬ n→i(# vals) + i ≤ i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i ']
Proof step 64:
i1 < i ∨ n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (addarray(r, ty, i0 + i + n→i(# vals), st)[r -- i1 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- i1 ']), ¬ i1 < i ∧ ¬ n→i(# vals) + i ≤ i1

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] → [i1, r, addarray(r, ty, i0 + i + n→i(# vals), st), i, r, vals] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [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 < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i1, r, addarray(r, ty, i0 + i + n→i(# vals), st), i, r, vals)]]