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Proof step 36 from proof infinite-append-lem (previous step)

(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)) ⊦ (ii(m) + n < ii(n0) + # lf(n0) ∧ ¬ ii(m) + n < ii(n0) ⊃ lf(n0)[ii(m) + n - ii(n0)];nf(ii(m) + n)) = lf(m)[n], n0 = 0, n0 = m, m = n0 + 1, lf(m) = []

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 37:
ii(m) + n < ii(n0) + # lf(n0) ∧ ¬ ii(m) + n < ii(n0), (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)) ⊦ lf(n0)[ii(m) + n - ii(n0)] = lf(m)[n], n0 = 0, n0 = m, m = n0 + 1, lf(m) = []
Proof step 56:
¬ ii(m) + n < ii(n0) + # lf(n0) ∨ ii(m) + n < ii(n0), (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)) ⊦ nf(ii(m) + n) = lf(m)[n], n0 = 0, n0 = m, m = n0 + 1, lf(m) = []

Rule argument

pos: right 1

Proof step 36 from proof infinite-append-lem (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

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