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Proof step 61 from proof multi-isarrayref (previous step)

i = 0 ∧ # ((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)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, is_arrayref (r, (addarray(refs .first, mktype_from_dims(ty, n→i(# ((n→i(# acc) + i) ' + ints0)) - 1), mkjavavalues(acc), st)[r -- _length]) .intval, addarray(refs .first, mktype_from_dims(ty, n→i(# ((n→i(# acc) + i) ' + ints0)) - 1), mkjavavalues(acc), st)), 0 ∈ ints0 .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
⊦ countrefs(0 ' + ints) = 1
Proof step 60:
posints(ints0), ∀ 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)))) ⊦ acc = [], ints0 = [], 0 ∈ ints0 .butlast, is_arrayref(r, n→i(# mkjavavalues(acc)), addarray(r, mktype_from_dims(ty, n→i(# ints0)), mkjavavalues(acc), st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _length ] ) = intval(n→i(# vals))], [CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPFORWARD : ⊦ # refs = 1 ∧ r ∈ refs → refs = r '], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPSEQ : ⊦ n→i(n) = 0 ↔ n = 0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1])]]