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Proof step 41 from proof multi-field (previous step)

# refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, ∀ r, st, ty, acc, 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 → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs '])) ⊦ fs ' = _length, fs ' = _type, (addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- fs ']) = st[r -- fs '], 0 ∈ (i0 ' + ints0) .butlast

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ # ints = 1 → addmultiarrays(refs, i, acc, ty, ints, st) = addarray(refs .first, ty, ints .first, st)
Proof step 34:
# (i0 ' + ints0) ≠ 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, ∀ r, st, ty, acc, 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 → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs '])) ⊦ fs ' = _length, fs ' = _type, (addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- fs ']) = st[r -- fs '], 0 ∈ (i0 ' + ints0) .butlast
Proof step 40:
# (i0 ' + ints0) = 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, ∀ r, st, ty, acc, 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 → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs '])) ⊦ fs ' = _length, fs ' = _type, (addarray(refs .first, ty, (i0 ' + ints0) .first, st)[r -- fs ']) = st[r -- fs '], 0 ∈ (i0 ' + ints0) .butlast

Rule argument

[crewrite-arg: addmultiarrays-base , F , [st, ints, ty, acc, i, refs] → [st, i0 ' + ints0, ty, acc, i, refs] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0 ' + ints0, ty, acc, i, refs)]]