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Proof step 69 from proof multi-isarrayref (previous step)

ints = i0 + ints0, n→i(# acc) + i = i0, # refs = i→n(countrefs(i ' + ints0)), r ∈ refs, posints(ints), 0 ≤ 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)))) ⊦ ints = [], is_arrayref(r, (addmultiarrays(refs, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, ints, st)), 0 ∈ ints .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
# 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, (addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)), 0 ∈ ((n→i(# acc) + i) ' + ints0) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' + ints ≠ []], [CSIMPSEQ : ⊦ i + ints = i ' + ints])]]