feat(bookspec): the five laws as Lean theorems (P13 step 4)

The first edition's five laws (debits equal credits; the accounting
equation; the trial balance balances; net income articulates to equity;
the cash-flow sections sum to the change in cash) are theorems in
bookspec/lean, ported from verify/lean (Basic, Entry, Statements, Closing,
Ledger under namespace Bookspec) and restated by name in Laws.lean, each a
statement about every reachable state of the books. Audit.lean prints
their axioms; the checker's lean.rs test fails on a sorry, a law not
audited, or any axiom beyond propext, Quot.sound and Classical.choice.
Money is Int, the exact count of the smallest unit: every law is a law of
addition, so the model is faithful to exact decimals.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HS8WZziDnyxunC23MUxrLp

bookspec/checker/tests/lean.rs

@@ -0,0 +1,93 @@
+//! The five laws are Lean theorems in `bookspec/lean` (P13 step 4), with
+//! no assumption beyond Lean's standard axioms.
+
+use std::path::{Path, PathBuf};
+use std::process::Command;
+
+const LAWS: [&str; 5] = [
+    "law_debits_equal_credits",
+    "law_accounting_equation",
+    "law_trial_balance",
+    "law_net_income_articulates",
+    "law_cash_flow_is_change_in_cash",
+];
+
+fn lean_dir() -> PathBuf {
+    Path::new(env!("CARGO_MANIFEST_DIR")).join("../lean")
+}
+
+/// Every law is stated in `Laws.lean`, audited in `Audit.lean`, and no
+/// file of the library says `sorry`.
+#[test]
+fn the_five_laws_are_stated_and_audited() {
+    let laws = std::fs::read_to_string(lean_dir().join("Bookspec/Laws.lean")).unwrap();
+    let audit = std::fs::read_to_string(lean_dir().join("Audit.lean")).unwrap();
+    for law in LAWS {
+        assert!(laws.contains(&format!("theorem {law}")), "{law} is stated");
+        assert!(
+            audit.contains(&format!("#print axioms {law}")),
+            "{law} is audited"
+        );
+    }
+    for entry in std::fs::read_dir(lean_dir().join("Bookspec")).unwrap() {
+        let path = entry.unwrap().path();
+        let text = std::fs::read_to_string(&path).unwrap();
+        for (i, line) in text.lines().enumerate() {
+            let code = line.split("--").next().unwrap();
+            assert!(
+                !code
+                    .split(|c: char| !c.is_alphanumeric() && c != '_')
+                    .any(|w| w == "sorry"),
+                "{}:{}: sorry",
+                path.display(),
+                i + 1
+            );
+        }
+    }
+}
+
+/// With Lean installed, the library builds and every law depends only on
+/// `propext`, `Quot.sound` and `Classical.choice`. Without it the test
+/// says so and passes: `mise install` provides Lean (`just prove` is
+/// where the machine is known to have it).
+#[test]
+fn the_laws_use_standard_axioms_only() {
+    let built = Command::new("lake")
+        .arg("build")
+        .current_dir(lean_dir())
+        .output();
+    let Ok(built) = built else {
+        eprintln!("lake is not installed: the Lean build is not checked here");
+        return;
+    };
+    assert!(
+        built.status.success(),
+        "lake build:\n{}",
+        String::from_utf8_lossy(&built.stdout)
+    );
+    let out = Command::new("lake")
+        .args(["env", "lean", "Audit.lean"])
+        .current_dir(lean_dir())
+        .output()
+        .unwrap();
+    let text = String::from_utf8_lossy(&out.stdout);
+    assert!(out.status.success(), "audit:\n{text}");
+    for law in LAWS {
+        let line = text
+            .lines()
+            .find(|l| l.contains(&format!("Bookspec.{law}'")))
+            .unwrap_or_else(|| panic!("{law} is not audited:\n{text}"));
+        for axiom in line
+            .split('[')
+            .nth(1)
+            .unwrap()
+            .trim_end_matches(']')
+            .split(", ")
+        {
+            assert!(
+                ["propext", "Quot.sound", "Classical.choice"].contains(&axiom.trim()),
+                "{law}: axiom {axiom}"
+            );
+        }
+    }
+}