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