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Proof step 65 from proof multi-lengthin (previous step)

# (i0 ' + ints0) = 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, r ∈ refs, posints(ints0), 0 ≤ i0, ∀ st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ 0 ∈ (i0 ' + ints0) .butlast, r -- _length ∈ addarray(refs .first, ty, (i0 ' + ints0) .first, st) ∧ is_integervalue(addarray(refs .first, ty, (i0 ' + ints0) .first, st)[r -- _length]) ∧ ¬ (addarray(refs .first, ty, (i0 ' + ints0) .first, st)[r -- _length]) .intval < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
⊦ countrefs(i ') = 1
Proof step 64:
i ≤ i0, 0 ≤ i, 0 ≤ i0, ∀ st, ty, acc, ints, i, r, refs0. # refs0 < 1 → ( true → ( r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ r -- _length ∈ addarray(r, ty, i0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ (addarray(r, ty, i, st) [r -- _length ] ) = intval(i)], [CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPFORWARD : ⊦ # refs = 1 ∧ r ∈ refs → refs = r '], [CSIMPSEQ : ⊦ ¬ i ∈ []], [CSIMPSEQ : ⊦ i ' .butlast = []], [CSIMPSEQ : ⊦ posints([])], [CSIMPSEQ : ⊦ ints + [] = ints], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ 1 = m + 1 ↔ m = 0], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0])]]