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Proof step 35 from proof addarrays-auto-22 (previous step)

2 ' + 2 ' ≠ [] ∧ n→i(# (r ' + r0 ' + r1 ')) = countrefs(2 ' + 2 ') ∧ posints(2 ' + 2 ') ⊦ addmultiarrays(r ' + r0 ' + r1 ', (2 ' + 2 ') .first, [], mktype_from_dims(ty, countdims(2 ' + 2 ', 0)), getdims(2 ' + 2 '), st) = addarray(r, mkarraytype(ty), refval(r0) ' + refval(r1) ', addarray(r0, ty, 2, addarray(r1, ty, 2, st)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ 0 < j → countdims(j ' + ints, i) = countdims(ints, i)
Proof step 7:
0 < i ⊦ countdims(((* i)) ', j) = j
Proof step 8:
⊦ 0 < j → getdims(j ' + ints) = j ' + getdims(ints)
Proof step 9:
⊦ 0 ≤ i → getdims(i ') = i '
Proof step 34:
3 = countrefs(2 ' + 2 ') ⊦ addmultiarrays(r ' + r0 ' + r1 ', 2, [], ty, 2 ' + 2 ', st) = addarray(r, mkarraytype(ty), refval(r0) ' + refval(r1) ', addarray(r0, ty, 2, addarray(r1, ty, 2, st)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ posints(i ') ↔ 0 ≤ i], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ i ' + ints ≠ []], [CSIMPSEQ : ⊦ mktype_from_dims(ty, 0) = ty], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0])]]