[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 41 from proof diag-theorem-butlast (previous step)

# nextl(0, a) = ii(1) + 1, 1 + ii(n) = # x, x[ii(m)] = lf(m).last, ii(0) = 0, ii(n0 + 1) = ii(n0) + # lf(n0 + 1) - 1, lf(m + 1) = nextl(m, x[ii(m)]), lf(n0 + 1) = nextl(n0, lf(n0).last), lf(0) = a ', lf(1) = nextl(0, a), nextl(0, a) = a ' + y, x to ii(1) + 1 = nextl(0, a), (x from ii(n0)) to # lf(n0 + 1) = lf(n0 + 1), a ∈ nextl(0, a), ii(1) ≤ ii(n), ii(n0 + 1) ≤ ii(n), n ≤ m, ∀ n, a. nextl(n, a) ≠ [] ∧ nextl(n, a).head = a, ∀ n. lf(n + 1) = nextl(n, lf(n).last) ∧ lf(n) ≠ [], ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ m. n ≤ m → lf(m + 1).tail = [] ∧ ii(m) = ii(n), ∀ n1. ii(n1 + 1) = ii(n1) + # lf(n1 + 1) - 1 ∧ ¬ ii(n) < ii(n1 + 1) ∧ (x from ii(n1)) to # lf(n1 + 1) = lf(n1 + 1) ⊦ lf(m) = [], lf(n0) = [], nextl(0, a) = [], x = [], lf(m + 1) = x[ii(m)] ' ∧ ii(n) = ii(m)

User applied rule all left

And obtained the following new goals

Proof step 42:
# nextl(0, a) = ii(1) + 1, 1 + ii(n) = # x, x[ii(m)] = lf(m).last, ii(n0 + 1) = ii(n0) + # lf(n0 + 1) - 1, ii(0) = 0, lf(1) = nextl(0, a), lf(0) = a ', lf(n0 + 1) = nextl(n0, lf(n0).last), lf(m + 1) = nextl(m, x[ii(m)]), nextl(0, a) = a ' + y, (x from ii(n0)) to # lf(n0 + 1) = lf(n0 + 1), x to ii(1) + 1 = nextl(0, a), a ∈ nextl(0, a), n ≤ m, ii(n0 + 1) ≤ ii(n), ii(1) ≤ ii(n), n ≤ m → lf(m + 1).tail = [] ∧ ii(m) = ii(n), ∀ n1. ii(n1 + 1) = ii(n1) + # lf(n1 + 1) - 1 ∧ ¬ ii(n) < ii(n1 + 1) ∧ (x from ii(n1)) to # lf(n1 + 1) = lf(n1 + 1), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextl(n, lf(n).last) ∧ lf(n) ≠ [], ∀ n, a. nextl(n, a) ≠ [] ∧ nextl(n, a).head = a ⊦ lf(n0) = [], lf(m) = [], nextl(0, a) = [], x = [], lf(m + 1) = x[ii(m)] ' ∧ ii(n) = ii(m)

Rule argument

pos: left 20 terms: m abort: F discard: T computed: T

Additional information

Used terms: m