diff --git a/Concurrent Systems/notes/10 - Consensus Implementation.md b/Concurrent Systems/notes/10 - Consensus Implementation.md
index 90c2049..17f85f4 100644
--- a/Concurrent Systems/notes/10 - Consensus Implementation.md	
+++ b/Concurrent Systems/notes/10 - Consensus Implementation.md	
@@ -39,4 +39,10 @@ If A wait-free implements binary consensus for n processes, then there exists a
 Assume by contradiction A wait-free, with processes p and q.
 
 By the previous result, it has an initial bivalent configuration C
--  let S be a sequence of operations s.t. C’ = S(C) is maximally bivalent (i.e., p(S(C)) is 0-valent and q(S(C)) is 1-valent, or viceversa)
+-  let S be a sequence of operations s.t. C’ = S(C) is maximally bivalent (i.e., p(C') is 0-valent and q(C') is 1-valent, or viceversa)
+	- partendo da C' posso ancora avere due possibili computazioni dove una decide 0 e una decide 1, ma è l'ultima configurazione in cui è possibile. Quelle successive sono monovalenti.
+
+p(C’) can be R1.read() or R1.write(v) and q(C’) can be R2.read() or R2.write(v’)
+
+1. if R1 != R2
+	- Whatever operations p and q issue, we have that q(p(C’)) = p(q(C’)) But q(p(C’)) is 0-val (because p(C’) is) whereas p(q(C’)) is 1-val