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Proof step 40 from proof multi-at-other (previous step)

¬ r ∈ r0 ' + refs1 ∧ # (r0 ' + refs1) = i→n(countrefs(i1 ' + (i1 ' + ints1) .rest)) ∧ i1 ' + ints1 ≠ [] ∧ 0 ≤ i1 ∧ posints(i1 ' + ints1) ∧ ¬ 0 ∈ (i1 ' + ints1) .butlast ∧ i1 ≤ (i1 ' + ints1) .first → (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- sk]) = st[r -- sk], (addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- sk ] ) = (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- sk]), # refs = 1 + i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), lastn(i→n(countrefs(i1 ' + ints1)), refs) = r0 ' + refs1, posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, ∀ sk, st, ty, acc, 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 → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- sk]) = st[r -- sk])) ⊦ (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- sk]) = st[r -- sk], 0 = i0, (~1) = i2, r ∈ refs, 0 ∈ (i1 ' + ints1) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
(addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- sk ] ) = (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- sk]), # refs = 1 + i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), lastn(i→n(countrefs(i1 ' + ints1)), refs) = r0 ' + refs1, posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, ∀ sk, st, ty, acc, 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 → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- sk]) = st[r -- sk])) ⊦ (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- sk]) = st[r -- sk], 0 = i0, (~1) = i2, r ∈ refs, 0 ∈ (i1 ' + ints1) .butlast, r ≠ r0 ∧ ¬ r ∈ refs1 ∧ 1 + # refs1 = i→n(countrefs(i1 ' + ints1))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ 0 ≤ i → ( posints(i ' + ints) ↔ posints(ints))], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (i ' + ints) .rest = ints], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)])]]