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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 in-dom-inter (conclusion) (back to tree)

⊦ a ∈ st → (a ∈ dom st ∩ s ↔ a ∈ s)

System applied rule normalize

And obtained the following new goals

Proof step 2:
¬(a ∈ dom st ∩ s ↔ a ∈ s), a ∈ st ⊦

Rule argument

Additional information

Proof step 2 from proof in-dom-inter (previous step) (back to tree)

¬(a ∈ dom st ∩ s ↔ a ∈ s), a ∈ st ⊦

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: Dom: ⊦ a ∈ dom st ↔ a ∈ st; int-c: ⊦ s ∩ s0 = s0 ∩ s; from specification set-union int-a: ⊦ (s ∩ s0) ∩ s1 = s ∩ s0 ∩ s1; from specification set-union ⊦ a ∈ s1 ∩ s2 ↔ a ∈ s1 ∧ a ∈ s2; (ws)

Proof Tree for in-dom-inter (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.