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Proof step 22 from proof move-initvals (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
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 -- n→i(# vals1) ', val0][r -- i ', val][r -- _length, intval(n→i(# vals1) + 1)]) = addarray(r, ty, (vals1 + val0 ')[i→n(i), val], st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]