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Proof step 6 from proof countdims-notneg (previous step)

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

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 5:
0 < i0, countdims(ints0, i) < 0, 0 ≤ i, ∀ i1. i1 < 0 ∨ 0 ≤ countdims(ints0, i1) ⊦

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], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (i, ints0, i0)]]