P3: assets' posted and scheduled depreciation, their bases, and the K-1 on the tax basis (defect 13, D-41)

Book value is cost less what the books posted; the schedule's figure is
apart. An asset's acquired date comes from its entry. Contributed
property keeps its section 723 carryover basis apart from its depreciable
basis (the lower of value and adjusted basis), with its 704(c) built-in
gain and method. The K-1 worksheet reports tax-basis capital (Form 1065
Item L) beside the book figures, leaving open what only the CPA knows.

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

crates/ledger-core/src/proofs.rs

@@ -1675,6 +1675,50 @@ fn true_up_reaches_the_target() {
     kani::cover!(down > 0, "depreciation past the day, credited back");
 }
 
+/// `kernel::basis_figures` (rules.md B-25), for every rule and every
+/// cost, adjusted basis and value within the bounds: a purchase
+/// depreciates from cost with no §723 basis or built-in gain; a
+/// contribution's §723 basis is the adjusted basis and its built-in gain
+/// the value less it (negative exactly when the basis exceeds the value);
+/// carryover depreciates from the basis, personal use from the lesser of
+/// value and basis (at most each, equal to one); no overflow is reachable.
+#[kani::proof]
+fn basis_figures_laws() {
+    use crate::assets::BasisRule;
+    let r: u8 = kani::any();
+    kani::assume(r < 3);
+    let rule = match r {
+        0 => BasisRule::Purchase,
+        1 => BasisRule::Carryover723,
+        _ => BasisRule::PersonalUseConversion,
+    };
+    let (cost, adjusted, fmv) = (any_amount(), any_amount(), any_amount());
+    kani::assume(cost > 0 && adjusted >= 0 && fmv >= 0);
+    let f = kernel::basis_figures(rule, cost, adjusted, fmv).expect("no overflow");
+    match rule {
+        BasisRule::Purchase => {
+            assert_eq!(f.depreciable_basis, cost);
+            assert!(f.tax_basis_723.is_none() && f.built_in_gain_704c.is_none());
+        }
+        _ => {
+            assert_eq!(f.tax_basis_723, Some(adjusted));
+            let g = f.built_in_gain_704c.expect("a contribution's gain");
+            assert_eq!(g, fmv - adjusted);
+            assert_eq!(g < 0, adjusted > fmv);
+            if rule == BasisRule::Carryover723 {
+                assert_eq!(f.depreciable_basis, adjusted);
+            } else {
+                assert!(f.depreciable_basis <= adjusted && f.depreciable_basis <= fmv);
+                assert!(f.depreciable_basis == adjusted || f.depreciable_basis == fmv);
+            }
+        }
+    }
+    kani::cover!(
+        rule == BasisRule::PersonalUseConversion && fmv < adjusted,
+        "personal use worth less than its basis: a built-in loss"
+    );
+}
+
 // ---------------------------------------------------------------------------
 // The checker itself
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