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Proof step 67 from proof multi-isarrayref (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
⊦ countrefs(i ') = 1
Proof step 66:
0 ≤ i, 0 ≤ n→i(# acc) + i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < 1 → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ is_arrayref(r, n→i(# acc) + i, addarray(r, ty, n→i(# acc) + i, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ intval(i) .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])]]