\[\begin{split}\newcommand{\as}{\kw{as}}
\newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)}
\newcommand{\case}{\kw{case}}
\newcommand{\cons}{\textsf{cons}}
\newcommand{\consf}{\textsf{consf}}
\newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)}
\newcommand{\emptyf}{\textsf{emptyf}}
\newcommand{\End}{\kw{End}}
\newcommand{\kwend}{\kw{end}}
\newcommand{\even}{\textsf{even}}
\newcommand{\evenO}{\textsf{even}_\textsf{O}}
\newcommand{\evenS}{\textsf{even}_\textsf{S}}
\newcommand{\Fix}{\kw{Fix}}
\newcommand{\fix}{\kw{fix}}
\newcommand{\for}{\textsf{for}}
\newcommand{\forest}{\textsf{forest}}
\newcommand{\Functor}{\kw{Functor}}
\newcommand{\In}{\kw{in}}
\newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)}
\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)}
\newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)}
\newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}}
\newcommand{\injective}{\kw{injective}}
\newcommand{\kw}[1]{\textsf{#1}}
\newcommand{\length}{\textsf{length}}
\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3}
\newcommand{\List}{\textsf{list}}
\newcommand{\lra}{\longrightarrow}
\newcommand{\Match}{\kw{match}}
\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})}
\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})}
\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})}
\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})}
\newcommand{\mto}{.\;}
\newcommand{\nat}{\textsf{nat}}
\newcommand{\Nil}{\textsf{nil}}
\newcommand{\nilhl}{\textsf{nil\_hl}}
\newcommand{\nO}{\textsf{O}}
\newcommand{\node}{\textsf{node}}
\newcommand{\nS}{\textsf{S}}
\newcommand{\odd}{\textsf{odd}}
\newcommand{\oddS}{\textsf{odd}_\textsf{S}}
\newcommand{\ovl}[1]{\overline{#1}}
\newcommand{\Pair}{\textsf{pair}}
\newcommand{\plus}{\mathsf{plus}}
\newcommand{\SProp}{\textsf{SProp}}
\newcommand{\Prop}{\textsf{Prop}}
\newcommand{\return}{\kw{return}}
\newcommand{\Set}{\textsf{Set}}
\newcommand{\Sort}{\mathcal{S}}
\newcommand{\Str}{\textsf{Stream}}
\newcommand{\Struct}{\kw{Struct}}
\newcommand{\subst}[3]{#1\{#2/#3\}}
\newcommand{\tl}{\textsf{tl}}
\newcommand{\tree}{\textsf{tree}}
\newcommand{\trii}{\triangleright_\iota}
\newcommand{\Type}{\textsf{Type}}
\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}}
\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}}
\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]}
\newcommand{\WFE}[1]{\WF{E}{#1}}
\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)}
\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}}
\newcommand{\with}{\kw{with}}
\newcommand{\WS}[3]{#1[] \vdash #2 <: #3}
\newcommand{\WSE}[2]{\WS{E}{#1}{#2}}
\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4}
\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}}
\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}}
\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}}
\newcommand{\zeroone}[1]{[{#1}]}
\end{split}\]
Basic proof writing
Coq is an interactive theorem prover, or proof assistant, which means
that proofs can be constructed interactively through a dialog between
the user and the assistant. The building blocks for this dialog are
tactics which the user will use to represent steps in the proof of a
theorem.
The first section presents the proof mode (the core mechanism of the
dialog between the user and the proof assistant). Then, several
sections describe the available tactics. One section covers the
SSReflect proof language, which provides a consistent alternative set
of tactics to the standard basic tactics. The last section documents
the Scheme family of commands, which can be used to extend the
power of the induction and inversion tactics.
Additional tactics are documented in the next chapter
Automatic solvers and programmable tactics.