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

max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n) = ∞, # nσ = ⌜m0⌝ + ⌜1⌝ , stutf(nσ), n < nσ[m0], ∞.n + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n ⊦ nσ[m0] = 0, nσ[∞.n + m + 1] = n + 1, max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 154:
⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n))
Proof step 155:
(∀ n0. ∃ n1. n0 < n1 ∧ ¬ m0 < n1 ∧ nσ[n1] = n) ∨ (∀ n0. ¬(¬ m0 < n0 ∧ nσ[n0] = n)), # nσ = ⌜m0⌝ + ⌜1⌝ , stutf(nσ), n < nσ[m0], ∞.n + m + 1 < max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n ⊦ nσ[m0] = 0, nσ[∞.n + m + 1] = n + 1, max∞(λ n0. ¬ m0 < n0 ∧ nσ[n0] = n + 1).n = 0

Rule argument

spec: inst: name: maxinf-inf seq: ⊦ max∞(np) = ∞ ↔ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n)) subst: [np] → [λ n0. ¬ m0 < n0 ∧ nσ[n0] = n] flags: rewrite, current

Additional information

Used terms: λ n0. ¬ m0 < n0 ∧ nσ[n0] = n