[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 172 from proof inv-get-inverse-between (previous step)

# nσ = ⌜m0⌝ + ⌜1⌝ , n1 + m + 1 < ∞.n, nσ[n1] < nσ[m0], stutf(nσ), n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, (∀ n. ∃ n0. n < n0 ∧ ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1) ∨ (∀ n. m0 < n ∨ nσ[n] ≠ nσ[n1] + 1) ⊦ ∞.n = 0, nσ[n1 + m + 1] = nσ[n1] + 1, nσ[m0] = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 173:
⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)
Proof step 174:
stutf(nσ) ∧ ⌜m0⌝ < # nσ ∧ nσ[n1] + 1 ≤ nσ[m0] → (∃ m1. m1 ≤ m0 ∧ nσ[m1] = nσ[n1] + 1), # nσ = ⌜m0⌝ + ⌜1⌝ , n1 + m + 1 < ∞.n, nσ[n1] < nσ[m0], stutf(nσ), n1 ≤ m0, ∀ m. ¬ m0 < m ∧ nσ[m] = nσ[n1] → ¬ n1 < m, (∀ n. ∃ n0. n < n0 ∧ ¬ m0 < n0 ∧ nσ[n0] = nσ[n1] + 1) ∨ (∀ n. m0 < n ∨ nσ[n] ≠ nσ[n1] + 1) ⊦ ∞.n = 0, nσ[n1 + m + 1] = nσ[n1] + 1, nσ[m0] = 0

Rule argument

spec: inst: name: stutf-alltaken seq: ⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n) subst: [nσ, m, n] → [nσ, m0, nσ[n1] + 1] flags: current, []

Additional information

Used terms: nσ, m0, nσ[n1] + 1