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