Reuse RHS of rule with conditions

Question

I need to create rule2 with the same right hand side of rule1. This RHS contains If statements (and in fact quite a few more things that are calculated with the matched symbols, before the final expression).

rule2 = LHS -> rule1[[2]] ignores the If statement, but works.

rule2 = LHS :> rule1[[2]] does not work (does not associate matched stuff on the LHS)

I cannot use Condition (/;), because it clashes with another function that adds another Condition to the Rule

Minimal example:

rule1 = F[X_,n_?(#>=2&),a_,b_,ind__] :> If[a===b || Length[{ind}]===0, CANCEL, n*G[X,n,a,b,ind] ]
rule2 = H[X_,n_?(#>=0&),a_,b_,ind__] -> (rule1[[2]]/.n->n+2)

F[A,3,a,b,j]/.rule1 (*3 G[A, 3, a, b, j]*)
H[A,3,a,a,j]/.rule2 (*should CANCEL because a==b*)

Any help would be so useful.

Answer 1

I think that it's likely you could improve this whole situation with a redesign. You're basically trying to simulate what happens with SetDelayed, and it's probably easier to just use SetDelayed. But without full context, I don't know how to prescribe that for you. So, in the meantime, what I would suggest is to pull out the duplicated piece (the right hand side of your rule1) into its own representation:

RHS[X_, n_, a_, b_, ind__] := If[a === b || Length[{ind}] === 0, CANCEL, n*G[X, n, a, b, ind]]

rule1A = F[X_, n_?(# >= 2 &), a_, b_, ind__] :> RHS[X, n, a, b, ind];
rule2A = H[X_, n_?(# >= 0 &), a_, b_, ind__] :> RHS[X, n + 2, a, b, ind];

F[A, 3, a, b, j] /. rule1A
(* 3 G[A, 3, a, b, j] *)

H[A, 3, a, a, j] /. rule2A
(* CANCEL *)