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Proof step 20 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, i0 ≤ n→i(# ar), # ar ≤ i→n(i1) ⊦ # ar = 0, ar[n0 % # ar] = a, # ar = 1, i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
0 ≤ i ⊦ ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i

Rule argument

[x0lemmaarg: spec-name: intnat instance-name: lemma-name: num-i2n-le-02 antecedent: 0 ≤ i succedent: ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i substlist: [i, m] → [i1, # ar] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 14)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i ≤ j → ¬ j < i])], [EXTRATERMS : (i1, # ar)]]