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Proof step 37 from proof multi-length-first (previous step)

# refs + 1 = i→n(countrefs(i ' + ints0)), 0 ≤ i, posints(ints0), 0 ≤ n→i(# acc) + i, ∀ st, ty, r, acc, ints, i, refs0. # refs0 < # refs → ( true → ( # refs0 + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs0, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first))) ⊦ (addmultiarrays(r ' + refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) = intval(n→i(# acc) + i), 0 ∈ ((n→i(# acc) + i) ' + 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 36:
# ((n→i(# acc) + i) ' + ints0) ≠ 1, # refs + 1 = i→n(countrefs(i ' + ints0)), 0 ≤ i, posints(ints0), 0 ≤ n→i(# acc) + i, ∀ st, ty, r, acc, ints, i, refs0. # refs0 < # refs → ( true → ( # refs0 + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs0, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first))) ⊦ (addmultiarrays(r ' + refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) = intval(n→i(# acc) + i), 0 ∈ ((n→i(# acc) + i) ' + ints0) .butlast

Rule argument

[crewrite-arg: addmultiarrays-base , F , [st, ints, ty, acc, i, refs] → [st, (n→i(# acc) + i) ' + ints0, ty, acc, i, r ' + refs] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ 1 = m + 1 ↔ m = 0], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ (addarray(r, ty, i, st) [r -- _length ] ) = intval(i)], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0])], [EXTRATERMS : (st, (n→i(# acc) + i) ' + ints0, ty, acc, i, r ' + refs)]]