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Proof step 211 from proof putarray-addarray-override (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 193:
is_indexkey(sk), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- sk]) = (addarray(r0, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)[r0 -- sk])
Proof step 210:
0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ is_indexkey(sk), (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- sk]) = (addarray(r0, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)[r0 -- sk])

Rule argument

[fma-arg: is_indexkey(sk)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (is_indexkey(sk))]]