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Proof step 30 from proof putAr-lastrec (previous step)

∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ putArray(val0 ' + vals0 + val ', r, i, st) = (putArray(val0 ' + vals0, r, i, st)[r -- (i + n→i(# (val0 ' + vals0))) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ putArray(val ' + vals, r, i, st) = (putArray(vals, r, i + 1, st)[r -- i ', val])
Proof step 29:
∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ putArray(val0 ' + vals0 + val ', r, i, st) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r -- (i + n→i(# (val0 ' + vals0))) ', val])

Rule argument

[crewrite-arg: putArray-rec , F , [st, i, r, vals, val] → [st, i, r, vals0, val0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i, r, vals0, val0)]]