(******************************** semantics ***********************************)
lemma sem_if: ∀sig.∀M1,M2,M3:TM sig.∀Rtrue,Rfalse,R2,R3,acc.
- M1 â\8a§ [acc: Rtrue,Rfalse] → M2 ⊨ R2 → M3 ⊨ R3 →
+ M1 â\8a¨ [acc: Rtrue,Rfalse] → M2 ⊨ R2 → M3 ⊨ R3 →
ifTM sig M1 M2 M3 acc ⊨ (Rtrue ∘ R2) ∪ (Rfalse ∘ R3).
#sig #M1 #M2 #M3 #Rtrue #Rfalse #R2 #R3 #acc #HaccR #HR2 #HR3 #t
cases (HaccR t) #k1 * #outc1 * * #Hloop1 #HMtrue #HMfalse