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Proof step 42 from proof multi-in-other (previous step)

i = 0 ∧ # (i0 ' + ints0) > 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ st, ty, acc, sk, 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 -- sk ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- sk ∈ st))) ⊦ r -- sk ∈ addarray(refs .first, mktype_from_dims(ty, n→i(# (i0 ' + ints0)) - 1), mkjavavalues(acc), st) ↔ r -- sk ∈ st, ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
⊦ countrefs(0 ' + ints) = 1
Proof step 41:
# refs = 1, posints(ints0), r -- sk ∈ addarray(refs .first, mktype_from_dims(ty, n→i(# ints0)), mkjavavalues(acc), st), 0 < i0, r ∈ addarray(refs .first, mktype_from_dims(ty, n→i(# ints0)), mkjavavalues(acc), st), ∀ st, ty, acc, sk, 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 -- sk ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- sk ∈ st))) ⊦ ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast, r -- sk ∈ st

Rule argument

[emptyarg]

Additional information

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