Merges two formulas term1 & term2 into a disjunction A Or B. If term1 and/or term2 occur more than once each, only one occurrence of each is merged. Let s1 have (sL, term1 |- sR) as its bottommost sequent and let s2 have (tL, term2 |- tR,) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL, term1 |- sR tL, term2 |- tR -------------------------------------- (OrLeft) sL, tL, term1 v term2 |- sR, tR
Merges two formulas term1 & term2 into a disjunction A Or B. If term1 and/or term2 occur more than once each, only one occurrence of each is merged. Let s1 have (sL, term1 |- sR) as its bottommost sequent and let s2 have (tL, term2 |- tR,) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL, term1 |- sR tL, term2 |- tR -------------------------------------- (OrLeft) sL, tL, term1 v term2 |- sR, tR
The left proof with A in the antecedent of its bottommost sequent.
The right proof with B in the antecedent of its bottommost sequent.
The left part of the disjunction in s1.
The right part of the disjunction in s2.
An LK proof with s1 & s2 as its two subtrees and (sL, tL, term1 v term2 |- sR, tR) as its bottommost sequent.
Merges two formulas A & B (marked by term1oc & term2oc in the antecedents of s1 & s2) into a disjunction A Or B.
Merges two formulas A & B (marked by term1oc & term2oc in the antecedents of s1 & s2) into a disjunction A Or B. This function merely returns the resulting sequent, not a proof.
The left sequent.
The right sequent.
The occurrence of A in s1.
The occurrence of B in s2.
The sequent (sL, tL, A v B |- sR, tR).
Merges two formulas A & B (marked by term1oc & term2oc in the antecedents of s1 & s2) into a disjunction A Or B. Let s1 have (sL, A |- sR) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL, A |- sR tL, B |- tR ------------------------------ (OrLeft) sL, tL, A v B |- sR, tR
Merges two formulas A & B (marked by term1oc & term2oc in the antecedents of s1 & s2) into a disjunction A Or B. Let s1 have (sL, A |- sR) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL, A |- sR tL, B |- tR ------------------------------ (OrLeft) sL, tL, A v B |- sR, tR
The left proof with A in the antecedent of its bottommost sequent.
The right proof with B in the antecedent of its bottommost sequent.
The occurrence of A in s1.
The occurrence of B in s2.
An LK proof with s1 & s2 as its two subtrees and (sL, tL, A v B |- sR, tR) as its bottommost sequent.
Returns the left subformula.
Returns the left subformula.
A formula of the form l Or r
l.
Returns the left subformula.
Returns the left subformula.
A formula of the form l Or r
r.