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Proof step 179 from proof putarray-addarray-override (previous step)

0 < i, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, i→n(i) ≤ # vals0, i0 < i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = vals0[i→n(i0)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 171:
⊦ j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)]
Proof step 178:
¬ (i ≤ i0 ∧ i0 < n→i(# vals) + i), 0 < i, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, i→n(i) ≤ # vals0, i0 < i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = vals0[i→n(i0)]

Rule argument

[speclemmaarg: , j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)] ,[i, st, j, r, vals] → [i0, addarray(r0, ty, vals0, st), i, r0, vals] ,F ,storearrays , ,putar-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i0, addarray(r0, ty, vals0, st), i, r0, vals)]]