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Proof step 47 from proof multi-isarrayref (previous step)

refs = r0 + refs1 ∧ refs ≠ [], # refs = (i→n(countrefs(i0 ' + ints1)) * i→n(i1) + 1) + i→n(countrefs(i0 ' + ints1)), i→n(countrefs(i0 ' + ints1)) ≤ # refs, r ∈ refs, posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, ∀ 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)))) ⊦ (~1) = n→i(# acc) + i1, (~1) = i1, is_arrayref (r, (addmultiarrays (r0 ' + firstn(i→n(countrefs(i0 ' + ints1)) * i→n(i1), refs1), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) .intval, addmultiarrays (r0 ' + firstn(i→n(countrefs(i0 ' + ints1)) * i→n(i1), refs1), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st))), 0 ∈ (i0 ' + ints1) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# refs1 = i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, i→n(countrefs(i0 ' + ints1)) ≤ 1 + # refs1, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # (r0 + refs1) → ( 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)))) ⊦ (~1) = n→i(# acc) + i1, (~1) = i1, 0 ∈ (i0 ' + ints1) .butlast, is_arrayref (r, (addmultiarrays (r0 ' + firstn(i→n(countrefs(i0 ' + ints1)) * i→n(i1), refs1), i1, lastn(i→n(countrefs(i0 ' + ints1)), r0 ' + refs1) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), r0 ' + refs1), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) .intval, addmultiarrays (r0 ' + firstn(i→n(countrefs(i0 ' + ints1)) * i→n(i1), refs1), i1, lastn(i→n(countrefs(i0 ' + ints1)), r0 ' + refs1) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), r0 ' + refs1), i0, [], ty, i0 ' + ints1, st))), r ≠ r0 ∧ ¬ r ∈ refs1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]