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Proof step 41 from proof pop-corr (previous step)

buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), buf .size = n→i(# buf .data), (buf .first + 1) % buf .size < 0, 0 < buf .size, buf .first < buf .size, 0 ≤ buf .first, buf .len ≤ buf .size, 0 ≤ buf .len ⊦ # buf .data = 0, buf .size = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
0 < j ⊦ i % ((* j)) < 0 ↔ i < 0 ∧ i % j ≠ 0

Rule argument

[x0lemmaarg: spec-name: int-div instance-name: lemma-name: mod-ls-zero antecedent: 0 < j succedent: i % ((* j)) < 0 ↔ i < 0 ∧ i % j ≠ 0 substlist: [j, i] → [buf .size, buf .first + 1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (buf .size, buf .first + 1)]]