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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 1 from proof size-succ (conclusion) (back to tree)

⊦ # σ < ⌜n⌝ + ⌜1⌝ ↔ ¬ ⌜n⌝ < # σ

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof size-succ (previous step) (back to tree)

¬(# σ < ⌜n⌝ + ⌜1⌝ ↔ ¬ ⌜n⌝ < # σ) ⊦

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ; size-inf: ⊦ # ⌜nf⌝ = ∞; stream freely generated by ⌜ ⌝, ⌜ ⌝;; ⊦ ¬ ∞ < n∞; (s) ⊦ ⌜m⌝ < ∞; (s) ⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝ ; (s) ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < 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

Proof Tree for size-succ (View conclusion)

The following image shows the proof tree of sequent calculus. The proved goal is at the bottom. You can click on the nodes to view additional rules. See here for details on colors in a proof tree.

the proof tree