diff --git a/Concurrent Systems/notes/9 - Consensus.md b/Concurrent Systems/notes/9 - Consensus.md
index 3653b4a..db9d6ce 100644
--- a/Concurrent Systems/notes/9 - Consensus.md	
+++ b/Concurrent Systems/notes/9 - Consensus.md	
@@ -225,13 +225,13 @@ bmv_propose(i,v) :=
 		res[k] <- BC[k].propose(b)
 	return value(res)
 ```
-(exercise: remove `∧ PROP[j][1..k-1]=res[1..k-1]` and execution in which a consensus property can be broken)
+(exercise: remove `∧ PROP[j][1..k-1]=res[1..k-1]` and show an execution in which a consensus property can be broken)
 
 *Proof:*
 - Wait freedom: trivial
 - Integrity: trivial
 - Agreement: by agreement of the h binary consensus objects
-- Validity: for all k, we prove that, if dec is the decided value, then there exists a j such that $p_j$ is participating (`PROP[j] ≠ ⊥`) and `dec[1...k] = PROP[j][1...k]`
+- Validity: for all k, we prove that, if `dec` is the decided value, then there exists a j such that $p_j$ is participating (`PROP[j] ≠ ⊥`) and `dec[1...k] = PROP[j][1...k]`
 	- by construction, P contains the k-th bits of the proposals whose first (k-1) bits coincide with the first k-1 bits decides so far:
 		- for every  b ∈ P, there exists a j such that `PROP[j] ≠ ⊥`,
 		- `PROP[j][1..k-1] = dec[1..k-1]` and `PROP[j][k] = b`