Cuts a common formula term1 (found in the succedent of s1 and the antecedent of s2) from two proofs s1 & s2. F is automatically determined. If term1 occurs more than once, only the first occurrence is cut. Let s1 have (sL |- sR, term1) as its bottommost sequent and let s2 have (tL, term1 |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, term1 tL, term1 |- tR --------------------------------- (Cut) sL, tL |- sR, tR
Cuts a common formula term1 (found in the succedent of s1 and the antecedent of s2) from two proofs s1 & s2. F is automatically determined. If term1 occurs more than once, only the first occurrence is cut. Let s1 have (sL |- sR, term1) as its bottommost sequent and let s2 have (tL, term1 |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, term1 tL, term1 |- tR --------------------------------- (Cut) sL, tL |- sR, tR
The left proof with term1 in the succedent of its bottommost sequent.
The right proof with term1 in the antecedent of its bottommost sequent.
An LK proof with s1 & s2 as its two subtrees and (sL, tL |- sR, tR) as its bottommost sequent.
Cuts a common formula F (marked by term1oc in the succedent of s1 and by term2oc in the antecedent of s2) from two proofs s1 & s2. This function merely returns the resulting sequent, not a proof. Let s1 have (sL |- sR, F) as its bottommost sequent and let s2 have (tL, F |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, F tL, F |- tR ------------------------------ (Cut) sL, tL |- sR, tR
Cuts a common formula F (marked by term1oc in the succedent of s1 and by term2oc in the antecedent of s2) from two proofs s1 & s2. This function merely returns the resulting sequent, not a proof. Let s1 have (sL |- sR, F) as its bottommost sequent and let s2 have (tL, F |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, F tL, F |- tR ------------------------------ (Cut) sL, tL |- sR, tR
The left sequent.
The right sequent.
The occurrence of F in s1.
The occurrence of F in s2.
The sequent (sL, tL |- sR, tR).
Cuts a common formula F (marked by term1oc in the succedent of s1 and by term2oc in the antecedent of s2) from two proofs s1 & s2. Let s1 have (sL |- sR, F) as its bottommost sequent and let s2 have (tL, F |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, F tL, F |- tR ------------------------------ (Cut) sL, tL |- sR, tR
Cuts a common formula F (marked by term1oc in the succedent of s1 and by term2oc in the antecedent of s2) from two proofs s1 & s2. Let s1 have (sL |- sR, F) as its bottommost sequent and let s2 have (tL, F |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, F tL, F |- tR ------------------------------ (Cut) sL, tL |- sR, tR
The left proof with F in the succedent of its bottommost sequent.
The occurrence of F in s1.
The occurrence of F in s2.
An LK proof with s1 & s2 as its two subtrees and (sL, tL |- sR, tR) as its bottommost sequent.