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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
m ≤ m0, n < n0 ⊦ m + n < m0 + n0
Proof step 40:
¬ (i→n(i0) ≤ # ar ∧ n < # ar), i→n(i0) + i→n(i1) = n0 % # ar + # ar, i→n(i0) + n = n0 + # ar, n0 % # ar < n0 + # ar, n0 % # ar < # ar, 0 < i1, n < i→n(i1), 0 ≤ i0 + i1, inv(mk(ar[n0 % # ar, 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), # ar ≤ n0, n0 % # ar < n0 ⊦ i→n(i0) + n < # ar + # ar, i1 = 0, # ar = 1, ar[n0 % # ar] = a

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: pls antecedent: m ≤ m0, n < n0 succedent: m + n < m0 + n0 substlist: [n0, m0, n, m] → [# ar, # ar, n, i→n(i0)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (# ar, # ar, n, i→n(i0))]]