Constructs a proof ending with a DefinitionRight rule. In it, a term aux is replaced by formula main, i.e. aux is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, aux ---------------- (DefinitionRight) sL |- sR, main
Constructs a proof ending with a DefinitionRight rule. In it, a term aux is replaced by formula main, i.e. aux is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, aux ---------------- (DefinitionRight) sL |- sR, main
The top proof with (sL |- sR, A) as the bottommost sequent.
The term to be replaced by its definition.
The formula with which aux is to be replaced.
An LK Proof ending with the new inference.
Replaces a term by its definition. In the returned sequent, a term A (marked by term1oc) is replaced by formula main, i.e. A is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, A --------------- (DefinitionRight) sL, main |- sR
Replaces a term by its definition. In the returned sequent, a term A (marked by term1oc) is replaced by formula main, i.e. A is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, A --------------- (DefinitionRight) sL, main |- sR
Sequent (sL |- sR, A).
The occurrence of A in s1.
The formula with which A is to be replaced.
The sequent (sL |- sR, main).
Constructs a proof ending with a DefinitionRight rule. In it, a term A (marked by term1oc) is replaced by formula main, i.e. A is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, A --------------- (DefinitionRight) sL |- sR, main
Constructs a proof ending with a DefinitionRight rule. In it, a term A (marked by term1oc) is replaced by formula main, i.e. A is defined as main. This rule does not check for contradictory definitions elsewhere in s1, and thus the burden of correct usage is on the programmer! Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof. The rule: (rest of s1) sL |- sR, A --------------- (DefinitionRight) sL |- sR, main
The top proof with (sL |- sR, A) as the bottommost sequent.
The occurrence of A in s1.
The formula with which A is to be replaced.
An LK Proof ending with the new inference.