P3: depreciation straight-line by days through the final month, schedules by day (defects 22, 9, D-37)

The final month takes what the months before leave, spread over its days;
a disposed asset stops on its disposal day. A skipped month is caught up
in the month the run is made; a reversed run un-posts its month. New
schedules spread by day; equal-months schedules must start on the 1st.
Amounts round to the currency's own minor unit. Kani and Lean proofs; an
exhaustive search over runs, reversals and disposals.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01T3gXMVt7XJPi6ens1or9Dj

verify/lean/Audit.lean

@@ -71,3 +71,21 @@ open Wanderbooks
 #print axioms capitalTarget_odd
 #print axioms partyTarget_odd
 #print axioms sumOver_movement_reversal
+#print axioms Prorate.cum_mono
+#print axioms Prorate.cum_le
+#print axioms Prorate.cum_full
+#print axioms Prorate.parts_telescope
+#print axioms Prorate.prorate_total
+#print axioms Prorate.prorate_nonneg
+#print axioms Prorate.part_within_a_unit
+#print axioms Prorate.roundUnit_near
+#print axioms Prorate.roundUnit_scale
+#print axioms Prorate.cum_near
+#print axioms Prorate.cum_dvd
+#print axioms Prorate.part_near
+#print axioms Prorate.chargeMid_eq_cum
+#print axioms Prorate.chargeLast_eq_cum
+#print axioms Prorate.chargeLast_start
+#print axioms Prorate.chargeLast_mono
+#print axioms Prorate.kernel_parts_total
+#print axioms Prorate.kernel_parts_nonneg