diff --git a/src/format.rs b/src/format.rs
index 3f71646..8cf3991 100644
--- a/src/format.rs
+++ b/src/format.rs
@@ -12,6 +12,9 @@ impl std::fmt::Debug for crate::project::StatementKind
 				=> write!(format, "completion(constraint)"),
 			crate::project::StatementKind::Assumption => write!(format, "assumption"),
 			crate::project::StatementKind::Assertion => write!(format, "assertion"),
+			crate::project::StatementKind::Lemma(None) => write!(format, "lemma"),
+			crate::project::StatementKind::Lemma(Some(crate::project::ProofDirection::Forward)) => write!(format, "lemma(forward)"),
+			crate::project::StatementKind::Lemma(Some(crate::project::ProofDirection::Backward)) => write!(format, "lemma(backward)"),
 		}
 	}
 }
diff --git a/src/format_tptp.rs b/src/format_tptp.rs
index eae4ecf..54715c0 100644
--- a/src/format_tptp.rs
+++ b/src/format_tptp.rs
@@ -1,10 +1,3 @@
-#[derive(Clone, Copy, Eq, Hash, PartialEq)]
-pub enum ProofDirection
-{
-	Forward,
-	Backward,
-}
-
 pub trait DisplayTPTP<'a, DisplayType>
 	where DisplayType: 'a + std::fmt::Debug + std::fmt::Display
 {
@@ -12,12 +5,14 @@ pub trait DisplayTPTP<'a, DisplayType>
 }
 
 pub fn is_statement_kind_conjecture(statement_kind: &crate::project::StatementKind,
-	proof_direction: ProofDirection) -> bool
+	proof_direction: crate::project::ProofDirection) -> bool
 {
 	match (proof_direction, statement_kind)
 	{
-		(ProofDirection::Forward, crate::project::StatementKind::Assertion) => true,
-		(ProofDirection::Backward, crate::project::StatementKind::Completion(_)) => true,
+		(crate::project::ProofDirection::Forward, crate::project::StatementKind::Assertion) => true,
+		(crate::project::ProofDirection::Backward, crate::project::StatementKind::Completion(_)) => true,
+		(_, crate::project::StatementKind::Lemma(None)) => true,
+		(proof_direction, crate::project::StatementKind::Lemma(Some(proof_direction_lemma))) => proof_direction == *proof_direction_lemma,
 		_ => false,
 	}
 }
@@ -242,13 +237,13 @@ struct FormulaDisplay<'a>(&'a foliage::Formula);
 struct StatementKindDisplay<'a>
 {
 	statement_kind: &'a crate::project::StatementKind,
-	proof_direction: ProofDirection,
+	proof_direction: crate::project::ProofDirection,
 }
 pub struct ProjectDisplay<'a>
 {
 	project: &'a crate::project::Project,
 	conjecture: &'a crate::project::Statement,
-	proof_direction: ProofDirection,
+	proof_direction: crate::project::ProofDirection,
 }
 
 impl<'a> DisplayTPTP<'a, VariableDeclarationDisplay<'a>> for foliage::VariableDeclaration
@@ -284,7 +279,7 @@ impl<'a> DisplayTPTP<'a, FormulaDisplay<'a>> for foliage::Formula
 }
 
 fn display_statement_kind_tptp<'a>(statement_kind: &'a crate::project::StatementKind,
-	proof_direction: ProofDirection)
+	proof_direction: crate::project::ProofDirection)
 	-> StatementKindDisplay<'a>
 {
 	StatementKindDisplay
@@ -295,7 +290,7 @@ fn display_statement_kind_tptp<'a>(statement_kind: &'a crate::project::Statement
 }
 
 pub fn display_project_with_conjecture_tptp<'a>(project: &'a crate::Project,
-	conjecture: &'a crate::project::Statement, proof_direction: ProofDirection)
+	conjecture: &'a crate::project::Statement, proof_direction: crate::project::ProofDirection)
 	-> ProjectDisplay<'a>
 {
 	ProjectDisplay
@@ -588,10 +583,17 @@ impl<'a> std::fmt::Debug for StatementKindDisplay<'a>
 		{
 			(crate::project::StatementKind::Axiom, _) => write!(format, "axiom, axiom"),
 			(crate::project::StatementKind::Assumption, _) => write!(format, "assumption, axiom"),
-			(crate::project::StatementKind::Completion(_), ProofDirection::Forward) => write!(format, "completion, axiom"),
-			(crate::project::StatementKind::Completion(_), ProofDirection::Backward) => write!(format, "completion, conjecture"),
-			(crate::project::StatementKind::Assertion, ProofDirection::Forward) => write!(format, "assertion, conjecture"),
-			(crate::project::StatementKind::Assertion, ProofDirection::Backward) => write!(format, "assertion, axiom"),
+			(crate::project::StatementKind::Completion(_), crate::project::ProofDirection::Forward) => write!(format, "completion, axiom"),
+			(crate::project::StatementKind::Completion(_), crate::project::ProofDirection::Backward) => write!(format, "completion, conjecture"),
+			(crate::project::StatementKind::Assertion, crate::project::ProofDirection::Forward) => write!(format, "assertion, conjecture"),
+			(crate::project::StatementKind::Assertion, crate::project::ProofDirection::Backward) => write!(format, "assertion, axiom"),
+			(crate::project::StatementKind::Lemma(None), _) => write!(format, "lemma, conjecture"),
+			(crate::project::StatementKind::Lemma(Some(proof_direction_lemma)), proof_direction) =>
+				match proof_direction == *proof_direction_lemma
+				{
+					true => write!(format, "lemma, conjecture"),
+					false => Ok(()),
+				},
 		}
 	}
 }
diff --git a/src/main.rs b/src/main.rs
index 511a92c..99196fe 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -20,7 +20,7 @@ fn backup_file_path(file_path: &std::path::Path) -> Result<std::path::PathBuf, a
 }
 
 fn find_conjecture<'a>(project: &'a ask_dracula::Project,
-	proof_direction: ask_dracula::format_tptp::ProofDirection)
+	proof_direction: ask_dracula::project::ProofDirection)
 	-> Option<&'a ask_dracula::project::Statement>
 {
 	for block in &project.blocks
@@ -38,7 +38,7 @@ fn find_conjecture<'a>(project: &'a ask_dracula::Project,
 }
 
 fn find_conjecture_mut<'a>(project: &'a mut ask_dracula::Project,
-	proof_direction: ask_dracula::format_tptp::ProofDirection)
+	proof_direction: ask_dracula::project::ProofDirection)
 	-> Option<&'a mut ask_dracula::project::Statement>
 {
 	for block in &mut project.blocks
@@ -149,9 +149,9 @@ fn main() -> Result<(), Box<dyn std::error::Error>>
 
 	let proof_directions = match matches.value_of("proof-direction").unwrap()
 	{
-		"forward" => vec![ask_dracula::format_tptp::ProofDirection::Forward],
-		"backward" => vec![ask_dracula::format_tptp::ProofDirection::Backward],
-		"both" => vec![ask_dracula::format_tptp::ProofDirection::Forward, ask_dracula::format_tptp::ProofDirection::Backward],
+		"forward" => vec![ask_dracula::project::ProofDirection::Forward],
+		"backward" => vec![ask_dracula::project::ProofDirection::Backward],
+		"both" => vec![ask_dracula::project::ProofDirection::Forward, ask_dracula::project::ProofDirection::Backward],
 		proof_direction => panic!("unrecognized proof direction “{}”", proof_direction),
 	};
 
diff --git a/src/parse.rs b/src/parse.rs
index 7d5307d..34573c9 100644
--- a/src/parse.rs
+++ b/src/parse.rs
@@ -42,6 +42,11 @@ fn statement_kind(i: &str) -> IResult<&str, crate::project::StatementKind>
 				|_| crate::project::StatementKind::Axiom,
 			),
 			map
+			(
+				tag("completion(constraint):"),
+				|_| crate::project::StatementKind::Completion(crate::project::CompletionTarget::Constraint),
+			),
+			map
 			(
 				preceded
 				(
@@ -71,13 +76,23 @@ fn statement_kind(i: &str) -> IResult<&str, crate::project::StatementKind>
 			),
 			map
 			(
-				tag("completion(constraint):"),
-				|_| crate::project::StatementKind::Completion(crate::project::CompletionTarget::Constraint),
+				tag("assumption:"),
+				|_| crate::project::StatementKind::Assumption,
 			),
 			map
 			(
-				tag("assumption:"),
-				|_| crate::project::StatementKind::Assumption,
+				tag("lemma(forward):"),
+				|_| crate::project::StatementKind::Lemma(Some(crate::project::ProofDirection::Forward)),
+			),
+			map
+			(
+				tag("lemma(backward):"),
+				|_| crate::project::StatementKind::Lemma(Some(crate::project::ProofDirection::Backward)),
+			),
+			map
+			(
+				tag("lemma:"),
+				|_| crate::project::StatementKind::Lemma(None),
 			),
 			map
 			(
diff --git a/src/project.rs b/src/project.rs
index b85c5c1..54f2e68 100644
--- a/src/project.rs
+++ b/src/project.rs
@@ -1,3 +1,10 @@
+#[derive(Clone, Copy, Eq, Hash, PartialEq)]
+pub enum ProofDirection
+{
+	Forward,
+	Backward,
+}
+
 #[derive(Eq, Hash, PartialEq)]
 pub enum CompletionTarget
 {
@@ -10,6 +17,7 @@ pub enum StatementKind
 {
 	Axiom,
 	Completion(CompletionTarget),
+	Lemma(Option<ProofDirection>),
 	Assumption,
 	Assertion,
 }