[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 29 from proof infinite-append-butlast (previous step)

ii(n0) = m0 + 1, ii(0) = 0, (σ from m0 + 1) to # x0 = ⌜x0⌝ , ii(n0 + 1) = (# x0 + m0) + 1, m0 + # lf(n0) - 1 = # x0 + m0, lf(n0) = a ' + x0, ⌜m0⌝ < # σ, ⌜# x0⌝ + ⌜m0⌝ < # σ, a ∈ lf(n0), ∀ n. σ[ii(n + 1) - 1] = lf(n + 1).first, ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ n. ii(n + 1) = ii(n) + # (n = 0 ⊃ lf(0);lf(n).rest) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # (n = 0 ⊃ lf(0);lf(n).rest) = ⌜(n = 0 ⊃ lf(0);lf(n).rest)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n).last = lf(n + 1).first ∧ lf(n) ≠ [], (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ ⌜σ[m0] '⌝ + (σ from m0 + 1) to # lf(n0) = ⌜lf(n0)⌝ , lf(n0) = []

User applied rule all left

And obtained the following new goals

Proof step 30:
ii(n0) = m0 + 1, ii(0) = 0, (σ from m0 + 1) to # x0 = ⌜x0⌝ , ii(n0 + 1) = (# x0 + m0) + 1, m0 + # lf(n0) - 1 = # x0 + m0, lf(n0) = a ' + x0, ⌜m0⌝ < # σ, ⌜# x0⌝ + ⌜m0⌝ < # σ, a ∈ lf(n0), σ[ii((n0 - 1) + 1) - 1] = lf((n0 - 1) + 1).first, ∀ n. σ[ii(n + 1) - 1] = lf(n + 1).first, ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ n. ii(n + 1) = ii(n) + # (n = 0 ⊃ lf(0);lf(n).rest) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # (n = 0 ⊃ lf(0);lf(n).rest) = ⌜(n = 0 ⊃ lf(0);lf(n).rest)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n).last = lf(n + 1).first ∧ lf(n) ≠ [], (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ ⌜σ[m0] '⌝ + (σ from m0 + 1) to # lf(n0) = ⌜lf(n0)⌝ , lf(n0) = []

Rule argument

pos: left 10 terms: n0 - 1 abort: F discard: F computed: F

Additional information

Used terms: n0 - 1