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Proof step 10 from proof pop-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ i ∧ 0 < j → i→n(i % j) = i→n(i) % i→n(j)
Proof step 9:
m ≠ 0 ⊦ (n0 % m + n1) % m = (n0 + n1) % m

Rule argument

[x0lemmaarg: spec-name: intnat instance-name: lemma-name: i2n-mod antecedent: succedent: 0 ≤ i ∧ 0 < j → i→n(i % j) = i→n(i) % i→n(j) substlist: [j, i] → [n→i(# ar), i0 + 1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 < m ↔ m ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i→n(n→i(n)) = n], [CSIMPSEQ : ⊦ m < n → n ≠ 0])], [EXTRATERMS : (n→i(# ar), i0 + 1)]]