Replaces a formula term1 with the conjunction term1 ∧ term2 in the antecedent of a sequent. If term1 occurs more than once, only one occurrence is replaced. The rule: (rest of s1) sL, term1 |- sR ----------------------- (AndLeft1) sL, term1 ∧ term2 |- sR
Replaces a formula term1 with the conjunction term1 ∧ term2 in the antecedent of a sequent. If term1 occurs more than once, only one occurrence is replaced. The rule: (rest of s1) sL, term1 |- sR ----------------------- (AndLeft1) sL, term1 ∧ term2 |- sR
The top proof with (sL, term1 |- sR) as the bottommost sequent.
The term to be replaced by the new conjunct.
The new term to add.
An LK Proof ending with the new inference.
Replaces a formula F (marked by term1oc) with the conjunction F ∧ term2 in the antecedent of a sequent.
Replaces a formula F (marked by term1oc) with the conjunction F ∧ term2 in the antecedent of a sequent. This function merely returns a sequent, not a proof.
The sequent (sL, F |- sR).
The occurrence of F in the antecedent of s1
The new term to add.
The sequent (sL, F ∧ term2 |- sR).
Replaces a formula F (marked by term1oc) with the conjunction F ∧ term2 in the antecedent of a sequent. The rule: (rest of s1) sL, F |- sR ------------------- (AndLeft1) sL, F ∧ term2 |- sR
Replaces a formula F (marked by term1oc) with the conjunction F ∧ term2 in the antecedent of a sequent. The rule: (rest of s1) sL, F |- sR ------------------- (AndLeft1) sL, F ∧ term2 |- sR
The top proof with (sL, F |- sR) as the bottommost sequent.
The occurrence of F in the antecedent of s1.
The new term to add.
An LK Proof ending with the new inference.
Returns the left subformula.
Returns the left subformula.
A formula of the form l And r
l.