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Proof step 22 from proof push-corr (previous step)

i→n(i0) + i→n(i1) = n0 + # ar, n0 % # ar = (i→n(i0) + n) % # ar, 0 ≤ (i0 + i1) % n→i(# ar), 0 ≤ i0, i1 ≤ n→i(# ar), i0 < n→i(# ar), inv(mk(ar, n→i(# ar), i0, i1)), i1 < n→i(# ar), inv(mk(ar[n0 % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1, n < i→n(i1), 0 < i1, # ar ≤ n0 ⊦ # ar = 0, ar[n0 % # ar] = a, # ar = 1, i1 = 0, i→n(i0) ≤ # ar ∧ i→n(i1) < # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
0 ≤ i ⊦ i→n(i) ≤ ((* m)) ↔ i ≤ n→i(m)
Proof step 21:
0 ≤ i0, i→n(i0) + i→n(i1) = n0 + # ar, n0 % # ar = (i→n(i0) + n) % # ar, 0 ≤ (i0 + i1) % n→i(# ar), 0 ≤ i0, i1 ≤ n→i(# ar), i0 < n→i(# ar), inv(mk(ar, n→i(# ar), i0, i1)), i1 < n→i(# ar), inv(mk(ar[n0 % # ar, a], n→i(# ar), i0, i1 + 1)), 0 ≤ i0 + i1, n < i→n(i1), 0 < i1, # ar ≤ n0 ⊦ # ar = 0, ar[n0 % # ar] = a, # ar = 1, i1 = 0, i0 ≤ n→i(# ar) ∧ i→n(i1) < # ar

Rule argument

[x0lemmaarg: spec-name: intnat instance-name: lemma-name: num-i2n-le antecedent: 0 ≤ i succedent: i→n(i) ≤ ((* m)) ↔ i ≤ n→i(m) substlist: [m, i] → [# ar, i0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 4, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (# ar, i0)]]