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Proof step 8 from proof move-initvals (previous step)

∀ val, st, ty, r, i, vals0. # vals0 < # vals1 + 1 → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ (addarray(r, ty, vals1, st)[r -- n→i(# vals1) ', val][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, (vals1 + val0 ')[# vals1, val], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ n = # vals → (vals + val ')[n, val0] = vals + val0 '
Proof step 7:
# vals1 = # vals1, ∀ val, st, ty, r, i, vals0. # vals0 < # vals1 + 1 → (true → (0 ≤ i ∧ i→n(i) < # vals0 → (addarray(r, ty, vals0, st)[r -- i ', val]) = addarray(r, ty, vals0[i→n(i), val], st))) ⊦ (addarray(r, ty, vals1, st)[r -- n→i(# vals1) ', val][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, vals1 + val ', st)

Rule argument

[speclemmaarg: ,n = # vals → (vals + val ')[n, val0] = vals + val0 ' ,[val0, n, val, vals] → [val, # vals1, val0, vals1] ,F ,list-del ,javavalues ,put-last ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, # vals1, val0, vals1)]]