Introduces an implication term1 -> term2, with term1 being in the succedent of s1 and B being in the antecedent of s2. Let s1 have (sL |- sR, term1) as its bottommost sequent and let s2 have (tL, term2 |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
Introduces an implication term1 -> term2, with term1 being in the succedent of s1 and B being in the antecedent of s2. Let s1 have (sL |- sR, term1) as its bottommost sequent and let s2 have (tL, term2 |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
The left proof with A in the succedent of its bottommost sequent.
The formula in s1.
The formula in s2.
An LK proof with s1 & s2 as its two subtrees and (sL, tL, term1 -> term2 |- sR, tR) as its bottommost sequent.
Introduces an implication A -> B, with A being marked by term1oc in the succedent of s1 and with B being marked by term2oc in the antecedent of s2. This function merely returns the resulting sequent, not a proof. Let s1 have (sL |- sR, A) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
Introduces an implication A -> B, with A being marked by term1oc in the succedent of s1 and with B being marked by term2oc in the antecedent of s2. This function merely returns the resulting sequent, not a proof. Let s1 have (sL |- sR, A) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
The left proof with A 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, A -> B |- sR, tR) as its bottommost sequent.
Introduces an implication A -> B, with A being marked by term1oc in the succedent of s1 and with B being marked by term2oc in the antecedent of s2. Let s1 have (sL |- sR, A) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
Introduces an implication A -> B, with A being marked by term1oc in the succedent of s1 and with B being marked by term2oc in the antecedent of s2. Let s1 have (sL |- sR, A) as its bottommost sequent and let s2 have (tL, B |- tR) as its bottommost sequent. The rule: (rest of s1) (rest of s2) sL |- sR, A tL, B |- tR ------------------------------ (ImpLeft) sL, tL, A -> B |- sR, tR
The left proof with A 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, A -> B |- sR, tR) as its bottommost sequent.
Returns the left subformula.
Returns the left subformula.
A formula of the form l Imp r
l.
Returns the right subformula.
Returns the right subformula.
A formula of the form l Imp r
r.