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Proof step 32 from proof addarrays-at-other (previous step)

n→i(# refs) = 1 + countrefs(ints0) * i0, posints(ints0), 0 ≤ i, 0 < i0 ⊦ (addmultiarrays(refs, i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st)[r -- sk]) = st[r -- sk], ints0 = [], # refs = 1 + i→n(countrefs(ints0)) * i→n(i0), 0 = i0, r ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
0 ≤ i ⊦ n→i(n) = i ↔ n = i→n(i)
Proof step 30:
⊦ abs(countrefs(ints)) = countrefs(ints)
Proof step 31:
⊦ 0 < i → i→n(1 + countrefs(ints) * i) = 1 + i→n(countrefs(ints)) * i→n(i)

Rule argument

[speclemmaarg: 0 ≤ i ,n→i(n) = ((* i)) ↔ n = i→n(i) ,[i, n] → [1 + countrefs(ints0) * i0, # refs] ,F ,intnat , ,num-n2i-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPFORWARD : ⊦ i < ((* j)) ∧ j < 0 → i < 0], [CSIMPSEQ : ⊦ i < 0 → ( n→i(m) = i + 1 ↔ m = 0 ∧ i = (~1))], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPSEQ : ⊦ i * j = (~1) ↔ abs(i) = 1 ∧ i = ~ j], [CSIMPSEQ : ⊦ ~ i = j ↔ i + j = 0], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i = 1 → i * j = j], [CSIMPSEQ : ⊦ i < j → ¬ j < i])], [EXTRATERMS : (1 + countrefs(ints0) * i0, # refs)]]