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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 one (conclusion) (back to tree)

⊦ unique_al(p ')

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof one (previous step) (back to tree)

¬ unique_al(p ') ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Rule argument

term: p

Additional information

Proof step 3 from proof one (previous step) (back to tree)

¬ unique_al((a, d) ') ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel>, name:unique-r, seq: ⊦ unique_al((a, d) ' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax), subst:[a, d, ax] → [a, d, []]

Additional information

Used simplifier rules: empty: ⊦ ¬ a ∈ []; unique-e: ⊦ unique_al([]); ⊦ x + [] = x; (s) a: ⊦ (x + y) + z = x + y + z; from specification polylist Used terms: a, d, []

Proof step 4 from proof one (previous step) (back to tree)

⊦ unique_al((a, d) ' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax)

Lemma unique-r

Proof Tree for one (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