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Proof step 20 from proof putArray-put (previous step)

∀ j, r, st, val. 0 ≤ j → (putArray(vals0, r, j, st)[r -- (j + n→i(# vals0)) ', val]) = putArray(vals0 + val ', r, j, st), 0 ≤ j ⊦ (putArray(val0 + vals0, r, j, st)[r -- (j + n→i(# (val0 + vals0))) ', val]) = putArray((val0 + vals0) + val ', r, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ (val + vals) + vals0 = val + (vals + vals0)
Proof step 19:
∀ j, r, st, val. 0 ≤ j → (putArray(vals0, r, j, st)[r -- (j + n→i(# vals0)) ', val]) = putArray(vals0 + val ', r, j, st), 0 ≤ j ⊦ (putArray(val0 + vals0, r, j, st)[r -- (j + n→i(# (val0 + vals0))) ', val]) = putArray(val0 + (vals0 + val '), r, j, st)

Rule argument

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

Additional information

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