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Proof step 30 from proof addarrays-auto-22 (previous step)

3 = countrefs(2 ' + 2 ') ⊦ addmultiarrays(firstn(2, r ' + r0 ' + r1 '), 1, r1 ', ty, 2 ' + 2 ', addarray(r1, ty, 2, st)) = addarray(r, mkarraytype(ty), refval(r0) ' + refval(r1) ', addarray(r0, ty, 2, addarray(r1, ty, 2, st)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
n ≠ 0 ⊦ firstn((* n), refs) = refs .first ' + firstn(n -1, refs .rest)
Proof step 29:
2 ≠ 0, 3 = countrefs(2 ' + 2 ') ⊦ addmultiarrays((r ' + r0 ' + r1 ') .first ' + firstn(2 -1, (r ' + r0 ' + r1 ') .rest), 1, r1 ', ty, 2 ' + 2 ', addarray(r1, ty, 2, st)) = addarray(r, mkarraytype(ty), refval(r0) ' + refval(r1) ', addarray(r0, ty, 2, addarray(r1, ty, 2, st)))

Rule argument

[speclemmaarg: n ≠ 0 ,firstn((* n), refs) = refs .first ' + firstn(n -1, refs .rest) ,[refs, n] → [r ' + r0 ' + r1 ', 2] ,F ,list-del ,references ,first-num ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + r0 ' + r1 ', 2)]]