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Ltac instantiate_pair := match goal with | |- context[ @fst ?A ?B ?x ] => is_evar x; let x1 := fresh in let x2 := fresh in evar (x1 : A); evar (x2 : B); unify x (@pair A B x1 x2); clear x1 x2 end. Ltac instantiate_pairs := repeat (instantiate_pair; simpl fst; simpl snd). Goal exists x : nat * nat, fst x = 1 /\ snd x = 2. eexists; instantiate_pairs; intuition. Qed. Goal exists x : (nat * nat * nat), fst (fst x) = 1 /\ snd (fst x) = 2 /\ snd x = 3. eexists; instantiate_pairs; intuition. Qed.