Replaced some cases instances with grind

InductiveVerification/Public.lean

@@ -33,6 +33,11 @@ noncomputable abbrev priSK (A : Agent) : Key := privateKey KeyMode.Signature A
 noncomputable abbrev pubK (A : Agent) : Key := pubEK A
 noncomputable abbrev priK (A : Agent) : Key := invKey (pubEK A)
 
+attribute [simp] pubEK
+attribute [simp] pubSK
+-- attribute [simp] priEK
+-- attribute [simp] priSK
+
 -- Axioms for private and public keys
 @[simp]
 axiom privateKey_neq_publicKey {b c : KeyMode} {A A' : Agent} :
@@ -320,7 +325,7 @@ lemma priK_in_initState {b : KeyMode} {A : Agent} :
     Msg.Key (privateKey b A) ∈ initState A := by
   induction A <;>
   simp [HasInitState.initState, initState, privateKey, pubEK, pubSK] <;>
-  cases b <;> simp[Spy_in_bad]
+  cases b <;> simp
 
 @[simp]
 lemma publicKey_in_initState {b : KeyMode} {A : Agent} {B : Agent} :
@@ -344,6 +349,7 @@ lemma analz_spies_pubK : Msg.Key (publicKey b A) ∈ analz (spies evs) := by
   exact analz.inj spies_pubK
 
 -- Spy sees private keys of bad agents
+@[grind .]
 lemma Spy_spies_bad_privateKey { h : A ∈ bad } : Msg.Key (privateKey b A) ∈ spies evs := by
   induction evs with
   | nil => simp_all [spies, knows, pubSK, pubEK]; cases b <;> tauto