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Proof step 13 from proof move-initvals (previous step)

¬ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i→n(i) = # vals1, 0 ≤ i, ∀ 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 + val ', st), i = n→i(# vals1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ m], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n = # vals → (vals + val ')[n, val0] = vals + val0 '], [CSIMPSEQ : ⊦ m ≤ n → (n ≤ m ↔ m = n)], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m])]]