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Proof step 21 from proof putAr-lastrec (previous step)

putArray(vals0 + val ', r, i + 1, st[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0]), ∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((1 + n→i(# vals0)) + i) ', val][r -- i ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ i + j + i0 = (i + j) + i0
Proof step 20:
putArray(vals0 + val ', r, i + 1, st[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0]), ∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0])

Rule argument

[speclemmaarg: ,i + j + i0 = (i + j) + i0 ,[i0, j, i] → [n→i(# vals0), 1, i] ,F ,int-basic2 , ,add-a ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (n→i(# vals0), 1, i)]]