Isabelle: The Next Seven Hundred Theorem Provers

Isabelle [2] is a theorem prover for a large class of logics. The object-logics are formalized within Isabelle’s meta-logic, which is intuitionistic higher-order logic with implication, universal quantifiers, and equality. The implication φ =⇒ ψ means ‘φ implies ψ’, and expresses logical entailment. The quantification ∧ x.φ means ‘φ is true for all x’, and expresses generality in rules and axiom schemes. The equality a ≡ b means ‘a equals b’, and allows new symbols to be defined as abbreviations.