Constructs a proof ending with a ExistsLeft rule. This function merely returns the resulting sequent, not a proof. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, A[y/x] |- sR
Constructs a proof ending with a ExistsLeft rule. This function merely returns the resulting sequent, not a proof. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, A[y/x] |- sR
The sequent (sL, A[y/x] |- sR).
The formula A[y/x], in which a free variable y is to be existentially quantified.
The resulting (Forall x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.
The eigenvariable to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.
The sequent (sL, Exists x.A |- sR).
Constructs a proof ending with a ExistsLeft rule. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, Exists x.A |- sR
Constructs a proof ending with a ExistsLeft rule. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, Exists x.A |- sR
The top proof with (sL, A[y/x] |- sR) as the bottommost sequent.
The occurrence of the formula A[y/x], in which a free variable y is to be existentially quantified.
The resulting (Exists x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.
The eigenvariable to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.
An LK Proof ending with the new inference.
Constructs a proof ending with a ExistsLeft rule. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, Exists x.A |- sR
Constructs a proof ending with a ExistsLeft rule. The rule: (rest of s1) sL, A[y/x] |- sR -------------------- (ExistsLeft) sL, Exists x.A |- sR
The top proof with (sL, A[y/x] |- sR) as the bottommost sequent.
The formula A[y/x], in which a free variable y is to be existentially quantified.
The resulting (Exists x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.
The eigenvariable to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.
An LK Proof ending with the new inference.