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Proof step 5 from proof countdims-zero-03 (previous step)

countdims(i0 ' + ints0, i) = 0, 0 < i, ∀ i1. i1 ≤ 0 ∨ countdims(ints0, i1) ≠ 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j → countdims(j ' + ints, i) = countdims(ints, i)
Proof step 3:
⊦ j ≤ 0 → countdims(j ' + ints, i) = i + n→i(# ints)
Proof step 4:
0 < i0, countdims(ints0, i) = 0, 0 < i, ∀ i1. i1 ≤ 0 ∨ countdims(ints0, i1) ≠ 0 ⊦

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0])], [EXTRATERMS : (i, ints0, i0)]]