From 714aba82a2d01604f72866d72ee9163ee19a3675 Mon Sep 17 00:00:00 2001
From: von-steinkirch
Date: Tue, 17 Jun 2025 11:29:50 -1000
Subject: [PATCH] add definig even number proof, more notes, and some refs
---
README.md | 17 +++-
docs/basic_concepts.md | 4 +
docs/formal_verification.md | 46 +++++++++++
docs/images/proof_assistant.png | Bin 0 -> 461180 bytes
src/proofs/DefiningEvenNumber.lean | 128 +++++++++++++++++++++++++++++
src/proofs/FermatLastTheorem.lean | 3 +
6 files changed, 196 insertions(+), 2 deletions(-)
create mode 100644 docs/formal_verification.md
create mode 100644 docs/images/proof_assistant.png
create mode 100644 src/proofs/DefiningEvenNumber.lean
diff --git a/README.md b/README.md
index 6a62093..8d34705 100644
--- a/README.md
+++ b/README.md
@@ -85,25 +85,38 @@ run any other file inside `src/example/` following its command inside `Makefile`
#### my notes
- [basics](docs/basic_concepts.md)
+- [formal veification](docs/formal_verification.md)
-#### learning lean
+#### learning lean and theorem proving
-- โ
[learn Lean from lean-lang.org](https://lean-lang.org/documentation/0)
+- โ
[learn Lean from lean-lang.org](https://lean-lang.org/documentation/)
+- โ
[Lean prover community](https://leanprover-community.github.io/)
- ๐ก [Lean 4 documentation](https://leanprover.github.io/lean4/doc/)
- ๐ก [mathematics in Lean](https://leanprover-community.github.io/mathematics_in_lean/C01_Introduction.html)
- ๐ก [theorem proving in Lean 4](https://leanprover.github.io/theorem_proving_in_lean4/)
+- ๐ก [the matrix cookbook](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf) with [code](https://github.com/eric-wieser/lean-matrix-cookbook)
+- ๐ก [the Lean 4 theorem prover and programming language](https://lean-lang.org/papers/lean4.pdf)
+- ๐ก [an extensible theorem proving frontend](https://lean-lang.org/papers/thesis-sebastian.pdf)
+- ๐ก [a metaprogramming framework for formal verification](https://lean-lang.org/papers/tactic.pdf)
#### useful
- [vscode/cursor plugin](https://marketplace.visualstudio.com/items?itemName=leanprover.lean4)
+- [mathlib algebra methods ref](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#Group)
+- [zulip Lean channel](https://leanprover.zulipchat.com/)
+- [moogle.ai (find theorems)](https://www.moogle.ai/)
#### applied examples
+- [Lean prover community's blog](https://leanprover-community.github.io/blog/) and [projects](https://leanprover-community.github.io/lean_projects.html)
+- [social choice theory in Lean (code)](https://github.com/asouther4/lean-social-choice?tab=readme-ov-file)
+- [the deep link equating math proofs and computer programs](https://www.quantamagazine.org/the-deep-link-equating-math-proofs-and-computer-programs-20231011/)
+ - *"types are fundamentally equivalent to logical propositions"*
- [AI safety via debate, by g. irving et al (2018)](https://arxiv.org/pdf/1805.00899)
- *"in the debate game, it is harder to lie than to refute a lie."*
\ No newline at end of file
diff --git a/docs/basic_concepts.md b/docs/basic_concepts.md
index f600ae2..808199e 100644
--- a/docs/basic_concepts.md
+++ b/docs/basic_concepts.md
@@ -369,6 +369,10 @@ def twice (f : Nat โ Nat) (a : Nat) := f (f a)
+* for instance, `(ยท + 2)` is syntax sugar for `(fun x => x + 2)`
+
+
+
---
## namespaces
diff --git a/docs/formal_verification.md b/docs/formal_verification.md
new file mode 100644
index 0000000..ef0c552
--- /dev/null
+++ b/docs/formal_verification.md
@@ -0,0 +1,46 @@
+# formal verification
+
+
+
+## tl; dr
+
+
+
+* formal methods are a set of techniques and specialized tools used to specify, design, and verify
+complex systems with mathematical rigor
+ - 1. specify: describe a system's desired behavior precisely
+ - 2. design: develop system components with assurance they'll work as intended
+ - 3. verify: prove or provide evidence that a system meets its specification
+
+
+
+---
+
+## proof assistant
+
+
+
+* a piece of software that provides a language for defining objects, specifying properties of these objects, and proving that these specifications hold (i.e., the system checks that these proofs are correct down to their logical foundation)
+* in a formalization, all definitions are precisely specified and all proofs are virtually guaranteed to be correct.
+
+
+
+
+
+
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