SUB_CONV : (conv -> conv)
|- (\x.t) = (\x.t')That is, SUB_CONV c "\x.t" applies c to the body of the abstraction "\x.t". If c is a conversion that maps "t1" to the theorem |- t1 = t1' and "t2" to the theorem |- t2 = t2', then the conversion SUB_CONV c maps an application "t1 t2" to the theorem:
|- (t1 t2) = (t1' t2')That is, SUB_CONV c "t1 t2" applies c to the both the operator t1 and the operand t2 of the application "t1 t2". Finally, for any conversion c, the function returned by SUB_CONV c acts as the identity conversion on variables and constants. That is, if "t" is a variable or constant, then SUB_CONV c "t" returns |- t = t.