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Proof step 54 from proof diag-theorem-butlast (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 13 terms: 0 abort: F discard: F computed: F

Additional information

Used simplifier rules: l: ⊦ a '.last = a; from specification list-last Used terms: 0