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smltheorem-provinghol

Exception on ACCEPT_TAC after THEN in HOL


I am trying to create a theorem named "absorptionRule" by packaging the tactics that are used to prove the goal !(p:bool) (q:bool). (p==>q) ==> p ==> p /\ q. However, I am getting an exception on ACCEPT_TAC. When I execute each tactic one-by-one, everything works fine.

val absorptionRule =  
TAC_PROOF(  
([],``!(p:bool) (q:bool).(p ==> q) ==> p ==> p /\ q``),  
REPEAT STRIP_TAC THEN  
ACCEPT_TAC(ASSUME ``p:bool``) THEN  
RES_TAC);  

Solution

  • The THEN tactical applies the second tactic to all the subgoals produced by the first tactic (source). But ACCEPT_TAC (ASSUME ``p:bool``) only applies to the first subgoal. You do not see any problem when you apply the tactics one-by-one because you never try to apply the ACCEPT_TAC to the second subgoal. The following solution uses THENL instead of THEN.

    val g1 = (([], ``!(p:bool) (q:bool). (p ==> q) ==> p ==> p /\ q``) : goal);
    val absorptionRule =
        TAC_PROOF (g1,
            REPEAT STRIP_TAC
            THENL [ACCEPT_TAC (ASSUME ``p:bool``), RES_TAC]);