Proof with simpl; auto.
intros H1 H2 H3. revert c0 H2. induction l... intros c0 H2.
inversion H1; apply IHl...
Qed.

Lemma rewrite_clause_in_space_sound a b p1 p2 sigma0 st :
clause_denote (PureClause nil [Eqv a b] p1 p2) st ->
space_denote sigma0 st ->
space_denote (map (rewrite_clause_in_space (PureClause nil [Eqv a b] p1 p2))
sigma0) st.