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Proof step 56 from proof infinite-append-lem (previous step)

ii(0) = 0, ii(m + 1) = ii(m) + # lf(m), (nf from ii(m)) to # lf(m) = lf(m), m < n0, n < # lf(m), ∀ m. m < n0 → ii(m + 1) = ii(m) + # lf(m) ∧ (nf from ii(m)) to # lf(m) = lf(m) ∧ (∀ m0. m0 ≤ m → ii(m0) ≤ ii(m)), ∀ m0. m0 ≤ m → ii(m0) ≤ ii(m), ¬ ii(m) + n < ii(n0) + # lf(n0) ∨ ii(m) + n < ii(n0) ⊦ lf(m) = [], m = n0 + 1, n0 = m, nf(ii(m) + n) = lf(m)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n])
Proof step 58:
#((nf from ii(m)) to # lf(m)) = # lf(m), ii(m + 1) = ii(m) + # lf(m), ii(0) = 0, n < # lf(m), m < n0, ∀ m0. m0 ≤ m → ii(m0) ≤ ii(m), ∀ m. m < n0 → ii(m + 1) = ii(m) + # lf(m) ∧ (nf from ii(m)) to # lf(m) = lf(m) ∧ (∀ m0. m0 ≤ m → ii(m0) ≤ ii(m)), ∀ n. n < #((nf from ii(m)) to # lf(m)) → ((nf from ii(m)) to # lf(m))[n] = lf(m)[n], ¬ ii(m) + n < ii(n0) + # lf(n0) ∨ ii(m) + n < ii(n0) ⊦ lf(m) = [], m = n0 + 1, n0 = m, nf(ii(m) + n) = lf(m)[n]

Rule argument

spec: list-del name: extension seq: ⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n]) subst: [y, x] → [lf(m), (nf from ii(m)) to # lf(m)] flags: <all paths>

Additional information

Used terms: lf(m), (nf from ii(m)) to # lf(m)