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Proof step 18 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 5:
⊦ val + vals = val ' + vals
Proof step 17:
∀ 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 = val ' + vals ,[vals, val] → [vals0, val0] ,F ,list ,javavalues ,c ]

Additional information

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