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Proof step 47 from proof diag-theorem-butlast (previous step)

lf(m + 1) = a0 ', ii(m) = ii(n), x[ii(n)] = lf(m).last, a0 ' = nextl(m, x[ii(n)]), 1 + ii(n) = # x, (x from ii(n0)) to # lf(n0 + 1) = lf(n0 + 1), ii(n0 + 1) = ii(n0) + # lf(n0 + 1) - 1, nextl(0, a) = a ' + y, lf(1) = nextl(0, a), lf(0) = a ', ii(0) = 0, x to ii(1) + 1 = nextl(0, a), lf(n0 + 1) = nextl(n0, lf(n0).last), # nextl(0, a) = ii(1) + 1, n ≤ m, ii(n0 + 1) ≤ ii(n), ii(1) ≤ ii(n), a ∈ nextl(0, a), ∀ n, a. nextl(n, a) ≠ [] ∧ nextl(n, a).first = a, ∀ n. lf(n + 1) = nextl(n, lf(n).last) ∧ lf(n) ≠ [], ∀ m, n. m ≤ n → 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) = [], x = [], lf(n0) = [], nextl(0, a) = [], a0 = x[ii(n)]

User applied rule all left

And closed the goal!

Rule argument

pos: left 19 terms: m, x[ii(n)] abort: F discard: F computed: T

Additional information

Used simplifier rules: first: ⊦ a '.first = a; from specification list Used terms: m, x[ii(n)]