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Proof step 25 from proof switch-array (previous step)

vals ≠ [], # vals = m + 1, ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < m + 1 → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ vals = [], r = r0, (addarray(r, ty, vals .butlast, addarray(r0, ty0, vals0, st))[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)]) = addarray(r0, ty0, vals0, addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# vals = m + 1, ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < m + 1 → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ r = r0, vals = [], (addarray(r, ty, vals .butlast, addarray(r0, ty0, vals0, st))[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)]) = addarray(r0, ty0, vals0, addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ n -1 = n - 1])]]