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Proof step 45 from proof multi-field (conclusion)

⊦ fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs ']

User applied rule induction

And obtained the following new goals

Proof step 44:
true, ∀ 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 ' ≠ _type ∧ fs ' ≠ _length ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs ']

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # refs, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# refs)]]