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Proof step 111 from proof lim-exists (previous step)

ii(0) = 0, # σσ = ∞, ii(n0 + 1) = ii(n0) + # lf(n0), mon(σσ), ∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1), ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ σσ = [], (nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0)) = nf to ii(n0 + 1), # σσ[0] = ∞, ∃ n. # σσ[n] = ∞

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n])
Proof step 113:
ii(0) = 0, # σσ = ∞, ii(n0 + 1) = ii(n0) + # lf(n0), mon(σσ), ∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1), ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ σσ = [], #((nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0))) = #(nf to ii(n0 + 1)) ∧ (∀ n. n < #((nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0))) → ((nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0)))[n] = (nf to ii(n0 + 1))[n]), # σσ[0] = ∞, ∃ n. # σσ[n] = ∞

Rule argument

spec: list-del inst: name: extension seq: ⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n]) subst: [y, x] → [nf to ii(n0 + 1), (nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0))] flags: rewrite

Additional information

Used terms: nf to ii(n0 + 1), (nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0))