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Proof step 23 from proof multi-fieldin (previous step)

# refs = 1 + i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, ∀ st, ty, acc, r, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- fs ' ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st))) ⊦ fs ' = _length, fs ' = _type, r -- fs ' ∈ addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, lastn(i→n(countrefs(i1 ' + ints1)), refs) .first ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i1 ' + ints1)), refs), i1, [], ty, i1 ' + ints1, st)) ↔ r -- fs ' ∈ st, 0 = i0, (~1) = i2, 0 ∈ (i1 ' + ints1) .butlast

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
⊦ countrefs(ints) ≠ 0
Proof step 22:
lastn(i→n(countrefs(i1 ' + ints1)), refs) = r0 + refs1 ∧ lastn(i→n(countrefs(i1 ' + ints1)), refs) ≠ [], # refs = 1 + i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, ∀ st, ty, acc, r, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- fs ' ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st))) ⊦ fs ' = _length, fs ' = _type, r -- fs ' ∈ addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i1 ' + ints1)), refs), i1, [], ty, i1 ' + ints1, st)) ↔ r -- fs ' ∈ st, 0 = i0, (~1) = i2, 0 ∈ (i1 ' + ints1) .butlast

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [lastn(i→n(countrefs(i1 ' + ints1)), refs), r0, refs1] ,T ,list-data ,references ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ lastn(n, refs) = [] ↔ n = 0], [CSIMPSEQ : ⊦ i→n(i) = 0 ↔ i = 0], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (lastn(i→n(countrefs(i1 ' + ints1)), refs), r0, refs1)]]