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Proof step 32 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 11:
⊦ val + vals = val ' + vals
Proof step 31:
∀ 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])

Rule argument

[speclemmaarg: ,val + vals = val ' + vals ,[vals, val] → [vals0, val0] ,F ,list ,javavalues ,c ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (vals0, val0)]]