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Proof step 27 from proof multi-mode (previous step)

2 ≤ ints .first, 0 ≤ ints .first, 0 < ints .first, ∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#(ints) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ # ints = 1, (addarraymultlist (refs .first, ty, addarraymultlist (r, ty, st[r -- (ints .first - 1) ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, i + n→i(# ints)))][r -- _length, intval(ints0 .first)], refs .rest, (ints .first - 1) ' + ints .rest, ints0, i), restn(i→n(countrefs2((ints .first - 1) ' + ints .rest)), refs .rest), ints .rest, ints0 .rest, i) [_mode ] ) = st[_mode], ints = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
ints = i0 + ints2, 2 ≤ i0, 0 ≤ i0, 0 < i0, ∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#(ints) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ # ints = 1, (addarraymultlist (refs .first, ty, addarraymultlist (r, ty, st[r -- (i0 - 1) ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, i + n→i(# ints)))][r -- _length, intval(ints0 .first)], refs .rest, (i0 - 1) ' + ints2, ints0, i), restn(i→n(countrefs2((i0 - 1) ' + ints2)), refs .rest), ints2, ints0 .rest, i) [_mode ] ) = st[_mode], ints = []

Rule argument

[speclemmaarg: ints ≠ [] ,i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0 ,[ints, i, ints0] → [ints, i0, ints2] ,T ,list-data ,intlista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ints ≠ [] ⊦ i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0])], [EXTRATERMS : (ints, i0, ints2)]]