[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 77 from proof lim-unique (previous step)

⌜m⌝ = # σ, ⌜m0⌝ = (⌜m⌝ + # σ1) + # σ2, ⌜n⌝ < # σσ, m0 < m, mon(σσ), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ), ∀ m. ¬ # σ < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ to m) + σ1 = σσ[n])), ∀ m1. ¬ m0 < m1 → (∃ n0. ⌜n0⌝ < # σσ ∧ (∃ σ1. (σσ[n] + σ2 to m1) + σ1 = σσ[n0])) ⊦ m = m0, m = 0, σσ = []

User applied rule structural induction

And obtained the following new goals

Proof step 78:
⌜m0⌝ = (⌜m⌝ + # σ1) + # σ2, ⌜m⌝ = # σ, ⌜m1⌝ = # σ2, m0 < m, ⌜n⌝ < # σσ, mon(σσ), ∀ m1. ¬ m0 < m1 → (∃ n0. ⌜n0⌝ < # σσ ∧ (∃ σ1. (σσ[n] + σ2 to m1) + σ1 = σσ[n0])), ∀ m. ¬ # σ < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ (∃ σ1. (σ to m) + σ1 = σσ[n])), ∀ n. ⌜n⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σ) ⊦ m = 0, m = m0, σσ = []

Rule argument

term: # σ2

Additional information

Used simplifier rules: natinf freely generated by ∞, ⌜ ⌝;;% ⊦ ∞ + ⌜m⌝ = ∞; (s)% ⊦ n∞ + ∞ = ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf% ⊦ ⌜m⌝ ≠ ∞; (s)