Constructs a proof ending with a EqLeft rule. In it, a formula term2 of the form A[T1/a] is replaced by formula main. This rule does not check for the correct use of the =-symbol. The burden of correct usage is on the programmer! The rule: (rest of s1) (rest of s2) sL |- a=b, sR tr, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
Constructs a proof ending with a EqLeft rule. In it, a formula term2 of the form A[T1/a] is replaced by formula main. This rule does not check for the correct use of the =-symbol. The burden of correct usage is on the programmer! The rule: (rest of s1) (rest of s2) sL |- a=b, sR tr, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
The left proof with the equarion a=b in the succent in its bottommost sequent.
The right proof with a formula A[T1/a] in the antecedent of its bottommost sequent, in which some term T1 has been replaced by the term a. Note that identical terms to T1 may occur elsewhere in A. These will not be changed. e.g. P([f(0)]) v -P(f(0)), where f(0) occurs twice, but T1 only refers to the bracketed f(0). This allows selective replacing of terms.
The formula (a=b) in s1.
The formula A[T1/a] in s2.
The formula A[T1/b], in which T1 has been replaced by b instead.
An LK Proof ending with the new inference.
Constructs a proof ending with a EqLeft rule. In it, a formula A (marked by term2oc) is replaced by formula main. This function merely returns the resulting sequent, not a proof. This rule does not check for the correct use of the =-symbol. The burden of correct usage is on the programmer! The rule: (s1) (s2) sL |- a=b, sR tr, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
Constructs a proof ending with a EqLeft rule. In it, a formula A (marked by term2oc) is replaced by formula main. This function merely returns the resulting sequent, not a proof. This rule does not check for the correct use of the =-symbol. The burden of correct usage is on the programmer! The rule: (s1) (s2) sL |- a=b, sR tr, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
The left sequent with the equarion a=b in its succent.
The right sequent with a formula A[T1/a] in the antecedent of its bottommost sequent, in which some term T1 has been replaced by the term a. Note that identical terms to T1 may occur elsewhere in A. These will not be changed. e.g. P([f(0)]) v -P(f(0)), where f(0) occurs twice, but T1 only refers to the bracketed f(0). This allows selective replacing of terms.
The occurrence (a=b) in s1.
The occurrence of A[T1/a] in s2.
The formula A[T1/b], in which T1 has been replaced by b instead.
The sequent (sL, A[T1/b], tL |- sR, tR).
Constructs a proof ending with a EqLeft rule. In it, a formula A (marked by term2oc) is replaced by formula main. This method tests whether the proposed auxiliary and main formulas differ in exactly one place. If so, it calls the next one with that position. The rule: (rest of s1) (rest of s2) sL |- a=b, sR tL, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
Constructs a proof ending with a EqLeft rule. In it, a formula A (marked by term2oc) is replaced by formula main. This method tests whether the proposed auxiliary and main formulas differ in exactly one place. If so, it calls the next one with that position. The rule: (rest of s1) (rest of s2) sL |- a=b, sR tL, A[T1/a] |- tR ------------------------------------ (EqLeft1) sL, A[T1/b], tL |- sR, tR
The left proof with the Eq a=b in the succedent in its bottommost sequent.
The right proof with a formula A[T1/a] in the antecedent of its bottommost sequent, in which some term T1 has been replaced by the term a. Note that identical terms to T1 may occur elsewhere in A. These will not be changed. e.g. P([f(0)]) v -P(f(0)), where f(0) occurs twice, but T1 only refers to the bracketed f(0). This allows selective replacing of terms.
The occurrence (a=b) in s1.
The occurrence of A[T1/a] in s2.
The formula A[T1/b], in which T1 has been replaced by b instead.
An LK Proof ending with the new inference.