Eliminates some theory axioms from proof
, namely those subsumed by formula
.
Eliminates some theory axioms from proof
, namely those subsumed by formula
.
A HOLFormula. Must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.
An LKProof.
An LKProof proof'
with the following properties: Every theory axiom in proof
that is subsumed by formula
is removed in proof'
and formula
may occur in the antecedent of the end sequent of proof'
.
Applies the proof transformation to an LKProof.
Applies the proof transformation to an LKProof.
The input proof.
The transformed proof.
A theory axiom with sequent A1,...,Ak :- B1,...,:Bn.
If A1,...,Ak :- B1,...,:Bn is subsumed by F, returns a proof of F, A1,...,Ak :- B1,...,:Bn. Otherwise the input axiom.
Eliminates some theory axioms from proof
, namely those subsumed by formula
.
Eliminates some theory axioms from proof
, namely those subsumed by formula
.
A HOLFormula. Must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.
An LKProof.
A pair (proof', conn)
with the following properties: Every theory axiom in proof
that is subsumed by formula
is removed in proof'
and formula
may occur in the antecedent of the end sequent of proof'
; conn
is an
OccConnector relating proof
and proof'
.
Applies the proof transformation to an LKProof.
Applies the proof transformation to an LKProof.
The input proof.
A pair consisting of the transformed proof and an OccConnector relating the two proofs.
Object for calling the
eliminateTheoryAxiom
transformation.