LP, the Larch Prover -- Proofs by well-founded induction

To prove a formula F by well-founded induction over a variable x of
sort S using a relation R that has been
asserted or proved to be
well founded, LP generates a single subgoal that involves proving the formula
F(xc) using the additional hypothesis R(x, xc) => F(x), where xc
is a new constant of sort S.

Example

assert well founded <
prove 0 + x = x by induction
New constant: xc
Induction subgoal: 0 + xc = xc
Induction hypothesis: x < xc => 0 + x = x