verifying-crypto-with-lean/preamble.tex

% ============================================================================
%  preamble.tex — shared style for "Verifying Cryptography with Lean 4"
%  A didactic identity: warm ink on soft paper, one confident accent, and a
%  small family of pedagogical boxes that each mean exactly one thing.
% ============================================================================
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage[margin=2.4cm,headsep=0.6cm]{geometry}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,positioning,shapes.geometric,calc,fit,backgrounds,decorations.pathreplacing,shapes.misc}
\usepackage[most]{tcolorbox}
\usepackage{listings}
\usepackage{microtype}
\usepackage{enumitem}
\usepackage{fancyhdr}
\usepackage{titlesec}
\usepackage{booktabs}
\usepackage[strings]{underscore} % plain _ works in text; math subscripts unaffected
\usepackage{hyperref}

% ---- palette -------------------------------------------------------------
% Ink is a deep blue-slate; the accent is a warm coral used sparingly; a
% calm teal marks "things that are true / proven". Neutrals carry a faint
% blue bias so nothing reads as unconsidered grey.
\definecolor{ink}{HTML}{1C2430}
\definecolor{ink2}{HTML}{51607A}
\definecolor{paper}{HTML}{FBFAF7}
\definecolor{accent}{HTML}{E4572E}     % coral — the one bold colour
\definecolor{accentsoft}{HTML}{FBE7DF}
\definecolor{proven}{HTML}{1E7F5C}     % teal-green — proven / correct
\definecolor{provensoft}{HTML}{E1F1EA}
\definecolor{warn}{HTML}{B4690E}       % amber — pitfalls
\definecolor{warnsoft}{HTML}{FBEFD8}
\definecolor{codebg}{HTML}{F3F1EC}
\definecolor{rule}{HTML}{DDE2E9}
\definecolor{kw}{HTML}{2B6CB0}
\definecolor{ty}{HTML}{6B46C1}
\definecolor{cmt}{HTML}{718096}
\definecolor{str}{HTML}{2F855A}

\hypersetup{colorlinks=true,linkcolor=accent,urlcolor=kw,citecolor=proven,
  pdftitle={Verifying Cryptography with Lean 4},pdfauthor={Fable 5}}

% ---- page furniture ------------------------------------------------------
\pagecolor{paper}
\color{ink}
\pagestyle{fancy}\fancyhf{}
\renewcommand{\headrulewidth}{0pt}
\fancyfoot[C]{\small\color{ink2}\thepage}
% single header element: chapter title only (no number prefix), no collisions
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\fancyhead[R]{\small\color{ink2}\scshape\leftmark}

\titleformat{\section}{\Large\bfseries\color{ink}}{\color{accent}\thesection}{0.7em}{}
\titleformat{\subsection}{\large\bfseries\color{ink}}{\color{accent}\thesubsection}{0.6em}{}
\setlength{\parskip}{0.55em}\setlength{\parindent}{0pt}

% ---- listings: Lean 4 and Rust ------------------------------------------
\lstdefinelanguage{Lean}{
  morekeywords={theorem,lemma,def,example,by,intro,intros,exact,apply,rw,simp,
    omega,decide,ring,constructor,rfl,have,let,fun,match,with,end,namespace,
    open,import,structure,inductive,instance,class,where,do,return,if,then,else,
    sorry,cases,induction,unfold,calc,show,from,at,using,Prop,Type,Nat,Int,Bool,True,False},
  sensitive=true,
  morecomment=[l]{--},
  morecomment=[s]{/-}{-/},
  morestring=[b]",
}
\lstdefinelanguage{RustL}{
  morekeywords={fn,let,mut,const,pub,struct,impl,for,in,if,else,match,return,
    u8,u16,u32,u64,u128,usize,i32,bool,self,Self,use,mod,where,unsafe,as},
  sensitive=true,
  morecomment=[l]{//},
  morecomment=[s]{/*}{*/},
  morestring=[b]",
}
\lstset{
  % render the Unicode symbols real Lean code uses
  literate={≠}{{$\neq$}}1 {∀}{{$\forall$}}1 {∃}{{$\exists$}}1
           {→}{{$\to$}}1 {↔}{{$\leftrightarrow$}}1 {∧}{{$\wedge$}}1
           {∨}{{$\vee$}}1 {¬}{{$\neg$}}1 {≤}{{$\leq$}}1 {≥}{{$\geq$}}1
           {ℕ}{{$\mathbb{N}$}}1 {ℤ}{{$\mathbb{Z}$}}1 {ℓ}{{$\ell$}}1
           {×}{{$\times$}}1 {∈}{{$\in$}}1 {∑}{{$\Sigma$}}1
           {α}{{$\alpha$}}1 {β}{{$\beta$}}1 {⟨}{{$\langle$}}1 {⟩}{{$\rangle$}}1
           {↦}{{$\mapsto$}}1 {⊢}{{$\vdash$}}1 {𝔽}{{$\mathbb{F}$}}1
           {₀}{{$_0$}}1 {₁}{{$_1$}}1 {₂}{{$_2$}}1 {²}{{$^2$}}1 {⁵}{{$^5$}}1
           {·}{{$\cdot$}}1 {←}{{$\leftarrow$}}1 {⟦}{{$[\![$}}1 {⟧}{{$]\!]$}}1
           {∘}{{$\circ$}}1 {≡}{{$\equiv$}}1 {∣}{{$\mid$}}1 {⁻¹}{{$^{-1}$}}1,
  basicstyle=\ttfamily\small\color{ink},
  keywordstyle=\color{kw}\bfseries,
  commentstyle=\color{cmt}\itshape,
  stringstyle=\color{str},
  numberstyle=\ttfamily\scriptsize\color{ink2},
  backgroundcolor=\color{codebg},
  frame=single, framerule=0pt, framesep=8pt,
  rulecolor=\color{codebg},
  xleftmargin=10pt, xrightmargin=6pt,
  breaklines=true, showstringspaces=false,
  columns=fullflexible, keepspaces=true,
  aboveskip=1em, belowskip=1em,
}
% Inline code: plain styled text (robust in tables/footnotes, unlike lstinline).
% Also safe inside math mode (wraps itself in \text there).
% Unicode symbols in inline code are handled by the declarations below.
\newcommand{\inlinecode}[1]{\ifmmode\text{\ttfamily\small #1}\else{\ttfamily\small #1}\fi}
\newcommand{\lean}[1]{\inlinecode{#1}}
\newcommand{\rust}[1]{\inlinecode{#1}}
\newcommand{\code}[1]{\inlinecode{#1}}
\DeclareUnicodeCharacter{2192}{\ensuremath{\to}}          % →
\DeclareUnicodeCharacter{2190}{\ensuremath{\leftarrow}}   % ←
\DeclareUnicodeCharacter{2194}{\ensuremath{\leftrightarrow}} % ↔
\DeclareUnicodeCharacter{2200}{\ensuremath{\forall}}      % ∀
\DeclareUnicodeCharacter{2203}{\ensuremath{\exists}}      % ∃
\DeclareUnicodeCharacter{2227}{\ensuremath{\wedge}}       % ∧
\DeclareUnicodeCharacter{2228}{\ensuremath{\vee}}         % ∨
\DeclareUnicodeCharacter{00AC}{\ensuremath{\neg}}         % ¬
\DeclareUnicodeCharacter{2260}{\ensuremath{\neq}}         % ≠
\DeclareUnicodeCharacter{2264}{\ensuremath{\leq}}         % ≤
\DeclareUnicodeCharacter{2265}{\ensuremath{\geq}}         % ≥
\DeclareUnicodeCharacter{22A2}{\ensuremath{\vdash}}       % ⊢
\DeclareUnicodeCharacter{00B7}{\ensuremath{\cdot}}        % ·
\DeclareUnicodeCharacter{2115}{\ensuremath{\mathbb{N}}}   % ℕ
\DeclareUnicodeCharacter{2124}{\ensuremath{\mathbb{Z}}}   % ℤ
\DeclareUnicodeCharacter{2113}{\ensuremath{\ell}}         % ℓ
\DeclareUnicodeCharacter{00D7}{\ensuremath{\times}}       % ×
\DeclareUnicodeCharacter{2208}{\ensuremath{\in}}          % ∈
\DeclareUnicodeCharacter{2211}{\ensuremath{\Sigma}}       % ∑
\DeclareUnicodeCharacter{2261}{\ensuremath{\equiv}}       % ≡
\DeclareUnicodeCharacter{2223}{\ensuremath{\mid}}         % ∣
\DeclareUnicodeCharacter{27E8}{\ensuremath{\langle}}      % ⟨
\DeclareUnicodeCharacter{27E9}{\ensuremath{\rangle}}      % ⟩
\DeclareUnicodeCharacter{1D53D}{\ensuremath{\mathbb{F}}}  % 𝔽
\DeclareUnicodeCharacter{2080}{\ensuremath{{}_0}}         % ₀
\DeclareUnicodeCharacter{2081}{\ensuremath{{}_1}}         % ₁
\DeclareUnicodeCharacter{2082}{\ensuremath{{}_2}}         % ₂
\DeclareUnicodeCharacter{00B2}{\ensuremath{{}^2}}         % ²
\DeclareUnicodeCharacter{2075}{\ensuremath{{}^5}}         % ⁵
\DeclareUnicodeCharacter{2713}{\ensuremath{\checkmark}}   % ✓
\DeclareUnicodeCharacter{2717}{\ensuremath{\times}}       % ✗
\DeclareUnicodeCharacter{207B}{\ensuremath{{}^{-}}}       % ⁻
\DeclareUnicodeCharacter{00B9}{\ensuremath{{}^{1}}}       % ¹
\DeclareUnicodeCharacter{00B3}{\ensuremath{{}^{3}}}       % ³
\DeclareUnicodeCharacter{2070}{\ensuremath{{}^{0}}}       % ⁰
\DeclareUnicodeCharacter{2074}{\ensuremath{{}^{4}}}       % ⁴
\DeclareUnicodeCharacter{2076}{\ensuremath{{}^{6}}}       % ⁶

% ---- pedagogical boxes: each means ONE thing ----------------------------
% BIG IDEA — the load-bearing concept of a section.
\newtcolorbox{bigidea}[1][]{enhanced,breakable,colback=accentsoft,
  colframe=accent,boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  fonttitle=\bfseries\color{paper},coltitle=paper,title={\faLightbulb\ The big idea},#1}
% TRY IT — a hands-on invitation to run something.
\newtcolorbox{tryit}[1][]{enhanced,breakable,colback=codebg,colframe=ink2,
  boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  fonttitle=\bfseries\color{paper},coltitle=paper,title={\faTerminal\ Try it yourself},#1}
% PITFALL — a trap, with its tell.
\newtcolorbox{pitfall}[1][]{enhanced,breakable,colback=warnsoft,colframe=warn,
  boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  fonttitle=\bfseries\color{paper},coltitle=paper,title={\faExclamationTriangle\ Pitfall},#1}
% AHA — an intuition that clicks.
\newtcolorbox{aha}[1][]{enhanced,breakable,colback=provensoft,colframe=proven,
  boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  fonttitle=\bfseries\color{paper},coltitle=paper,title={\faStar\ Aha},#1}
% CHECKPOINT — end-of-chapter self-check.
\newtcolorbox{checkpoint}[1][]{enhanced,breakable,colback=white,colframe=ink,
  boxrule=0.6pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  fonttitle=\bfseries\color{paper},coltitle=paper,title={\faFlagCheckered\ Checkpoint},#1}

% Poor-man's icons (fontawesome may be absent): draw tiny glyphs with text.
\providecommand{\faLightbulb}{\raisebox{-1pt}{\small$\ast$}}
\providecommand{\faTerminal}{\raisebox{-1pt}{\small\ttfamily>\_}}
\providecommand{\faExclamationTriangle}{\raisebox{-1pt}{\small$\triangle$}}
\providecommand{\faStar}{\raisebox{-1pt}{\small$\star$}}
\providecommand{\faFlagCheckered}{\raisebox{-1pt}{\small$\bowtie$}}

% ---- math shortcuts the whole book uses ---------------------------------
\newcommand{\F}{\mathbb{F}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Fp}{\mathbb{F}_p}
\newcommand{\Zmod}[1]{\mathbb{Z}/#1\mathbb{Z}}
% double-bracket "denotation" delimiters without stmaryrd
\newcommand{\denote}[1]{\ensuremath{[\mkern-3.3mu[ #1 ]\mkern-3.3mu]}}

% WORKED EXAMPLE — pen and paper, with the real numbers.
% Distinct look: white page, thick left margin rule like a notebook.
\newtcolorbox{worked}[1]{enhanced,breakable,colback=white,colframe=ink2,
  boxrule=0.4pt,leftrule=2.6pt,arc=1pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
  colbacktitle=codebg,coltitle=ink,
  fonttitle=\bfseries,title={\pennib\ Pen and paper: #1}}
\providecommand{\pennib}{\raisebox{-1pt}{\small$\angle$}}

% exercises
\newcounter{exc}[section]
\newcommand{\exercise}[1]{\refstepcounter{exc}\smallskip\noindent%
  {\bfseries\color{accent}Exercise \thechapter.\theexc.}\ #1\smallskip}

% solutions — immediately after each chapter's exercises.
% Every solution leads with the PATHWAY (how to find it), then the answer.
\newcommand{\solhead}[1]{\medskip\noindent%
  {\bfseries\color{proven}Solution #1.}\ }
\newcommand{\pathway}{\par\smallskip\noindent{\itshape\color{ink2}Pathway.}\ }
\newcommand{\answer}{\par\smallskip\noindent{\itshape\color{ink2}Answer.}\ }
\newcommand{\solutionsintro}{\noindent\begingroup\small\color{ink2}%
Attempt every exercise before reading on --- a pathway teaches
ten times as much after you have been genuinely stuck. Each solution
below starts with the \emph{pathway} (how you find the answer) and only
then the answer itself.\endgroup\par\medskip}