diff --git a/restructuring/README_jonathan.md b/restructuring/README_jonathan.md
index 12df31f3538efd2807b4f0c6f3dd57f431219596..5413d47d409bb1a3acd3526b90cd2552d46fba8b 100644
--- a/restructuring/README_jonathan.md
+++ b/restructuring/README_jonathan.md
@@ -131,14 +131,39 @@ and further development suggestions
### /restructuring/analysis/analysis_up_to_t/schedulability_up_to_t.v

It defines what it means to be a upper or lower response time bound until t,
- and then shows the equivalence between being a bound up ot t for all t and
- being a general time bound.
+ and then shows the equivalence between being a bound up ot t for all t and being a general time bound.
### /restructuring/analysis/analysis_up_to_t/cpa_temporal_step.v

- It defines what it means to be a upper or lower response time bound until t,
- and then shows the equivalence between being a bound up ot t for all t and
- being a general time bound.
+ It uses the abstract model defined in simple_abstracted.v.
+ The redundant definition of task_input_model and task_model_correct_until_t
+ should allow tasks to follow different types of arrival models.
+
+ Its purpose is the "final result", which states that if all conditions are met,
+ the WCRTs given by CPA will indeed be upper bounds on the response time for each task.
+
+ This uses 2 hypothesis meant to provide analysis on a propagationnal property of the schedule, and an analysis on WCRT.
+ They have yet to be proved in the exemple of the periodic_jitter_model.
+
+ ### /restructuring/analysis/analysis_up_to_t/periodic_jitter_propagation_up_to_t.v

+
+ There are two sections here.
+
+ In the first one, there is a proof of the propagatability of the finite
+ periodic jitter model, very similar to the one in periodic_jitter_same_law.
+ However the third hypothesis of that model is thrown away since we use the
+ 2 hypothesis finite model.
+
+ In the second one, the above result is used to prove that if all task follow a
+ periodic with jitter arrival model, and the system verify some reasonnable hypothesis,
+ then the result of CPA will be correct.
+
+ The analysis giving the correction of WCRTs is not done yet.
+
+ ### /restructuring/analysis/analysis_up_to_t/up_to_t_definitions.v

+
+ some definitions of properties that were defined indefinitely that now
+ have an equivalent up to t.
## III) Suggestions