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Proof step 9 from proof getcountdims (previous step)

∀ i. n→i(# getdims(ints0)) + countdims(ints0, i) = n→i(# ints0) + i ⊦ countdims(i0 ' + ints0, i) + n→i(# getdims(i0 ' + ints0)) = (1 + n→i(# ints0)) + i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j → countdims(j ' + ints, i) = countdims(ints, i)
Proof step 4:
⊦ j ≤ 0 → getdims(j ' + ints) = 0 '
Proof step 5:
⊦ j ≤ 0 → countdims(j ' + ints, i) = i + n→i(# ints)
Proof step 8:
0 < i0, ∀ i. n→i(# getdims(ints0)) + countdims(ints0, i) = n→i(# ints0) + i ⊦ countdims(ints0, i) + n→i(# getdims(i0 ' + ints0)) = (1 + n→i(# ints0)) + i

Rule argument

[crewrite-arg: countdims-rec, F, [i, ints, j] → [i, ints0, i0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRATERMS : (i, ints0, i0)]]