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Proof step 14 from proof multi-mode (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
ints = i0 + ints2, i0 = 1, ∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#(ints) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ ints = [], (addarraymultlist (refs .first, ty, st[r -- 0 ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, i + n→i(# ints)))][r -- _length, intval(ints0 .first)], refs .rest, ints2, ints0 .rest, i) [_mode ] ) = st[_mode], # ints = 1

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)]]