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Proof step 19 from proof move-initvals (previous step)

0 ≤ i, i→n(i) ≤ # 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 -- i ', val][r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, (vals1 + val0 ')[i→n(i), val], st), i = n→i(# vals1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n < # vals → (vals + val ')[n, val0] = vals[n, val0] + val '
Proof step 13:
¬ i→n(i) < # vals1, 0 ≤ i, i→n(i) ≤ # 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 -- i ', val][r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, (vals1 + val0 ')[i→n(i), val], st), i = n→i(# vals1)
Proof step 18:
i→n(i) < # vals1, 0 ≤ i, i→n(i) ≤ # 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 -- i ', val][r -- n→i(# vals1) ', val0][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, vals1[i→n(i), val] + val0 ', st), i = n→i(# vals1)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, i→n(i), val0, vals1)]]