object makeTheoryAxiomsExplicit
Given a list of formulas Π, this transforms a proof π of Σ :- Δ into a proof π' of Π, Σ :- Δ.
It replaces theory axioms on sequents S that are subsumed by Π with propositional proofs of Π, S.
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- makeTheoryAxiomsExplicit
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- def apply(proof: LKProof)(implicit ctx: Context): LKProof
- def apply(formulas: Formula*)(proof: LKProof): LKProof
Eliminates some theory axioms from
proof
, namely those subsumed byformulas
.Eliminates some theory axioms from
proof
, namely those subsumed byformulas
.- formulas
A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.
- proof
An LKProof.
- returns
An LKProof
proof'
with the following properties: Every theory axiom inproof
that is subsumed byformulas
is removed inproof'
and elements offormula
may occur in the antecedent of the end sequent ofproof'
.
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- def withSequentConnector(formulas: Formula*)(proof: LKProof): (LKProof, SequentConnector)
Eliminates some theory axioms from
proof
, namely those subsumed byformulas
.Eliminates some theory axioms from
proof
, namely those subsumed byformulas
.- formulas
A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.
- proof
An LKProof.
- returns
A pair
(proof', conn)
with the following properties: Every theory axiom inproof
that is subsumed byformulas
is removed inproof'
and elements offormulas
may occur in the antecedent of the end sequent ofproof'
;conn
is an SequentConnector relatingproof
andproof'
.
This is the API documentation for GAPT.
The main package is gapt.