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Proof step 29 from proof push-corr (previous step)

i→n(i1) = # ar + n, inv(mk(ar[i→n(i0) + n, a], n→i(# ar), i0, i1 + 1)), i1 < n→i(# ar), inv(mk(ar, n→i(# ar), i0, i1)), i0 < n→i(# ar), i1 ≤ n→i(# ar), 0 ≤ i0, 0 ≤ (i0 + i1) % n→i(# ar), i→n(i0) + n < # ar, 0 < i1, n < i→n(i1), 0 ≤ i0 + i1 ⊦ ar[i→n(i0) + n] = a, i1 = 0, # ar = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: intnat instance-name: lemma-name: num-n2i-ls-02 antecedent: 0 ≤ i succedent: ((* i)) < n→i(n) ↔ i→n(i) < n substlist: [n, i] → [# ar, i1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPFORWARD : ⊦ m < n ∧ n < n0 → m +1 < n0], [CSIMPFORWARD : ⊦ n < n0 ∧ n0 < n1 → n < n1], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ m + n < m])], [EXTRATERMS : (# ar, i1)]]