This version creates an axiom for the equation.
This version of the rule operates on formulas instead of occurrences.
This version of the rule operates on formulas instead of occurrences. It will attempt to find appropriate occurrences in the premises.
A proof ending with term1oc in the succedent.
A proof ending with term2oc in the antecedent.
An equation s = t.
A formula A.
A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.
A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.
A sequent with term1oc in the succedent.
A sequent with term2oc in the antecedent.
An equation s = t.
A formula A.
A position such that A(pos) = s or A(pos) = t
A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which replacement is sensible.
A sequent with term1oc in the succedent.
A sequent with term2oc in the antecedent.
An equation s = t.
A formula A.
A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.
A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.
A proof ending with term1oc in the succedent.
A proof ending with term2oc in the antecedent.
An equation s = t.
A formula A.
A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.
A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.
A proof ending with term1oc in the succedent.
A proof ending with term2oc in the antecedent.
An equation s = t.
A formula A.
A position such that A(pos) = s or A(pos) = t
A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which replacement is sensible.
This macro rule unifies EquationLeft1Rule and EquationLeft2Rule by automatically choosing the appropriate rule.