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Yiyun Liu 2025-03-06 16:20:32 -05:00
parent 96b3139726
commit 6f154cc9c6
2 changed files with 34 additions and 4 deletions
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16
theories/termination.v
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@ -264,3 +264,19 @@ Proof.
have {}nfb0 : HRed.nf a1 by sfirstorder use:hne_no_hred.
hauto lq:on use:term_metric_ind, algo_dom_r_algo_dom db:adom.
Qed.
Lemma sn_term_metric (a b : PTm) : SN a -> SN b -> exists k, term_metric k a b.
Proof.
move /LoReds.FromSN => [va [ha0 ha1]].
move /LoReds.FromSN => [vb [hb0 hb1]].
eapply relations.rtc_nsteps in ha0.
eapply relations.rtc_nsteps in hb0.
hauto lq:on unfold:term_metric solve+:lia.
Qed.
Lemma sn_algo_dom a b : SN a -> SN b -> algo_dom_r a b.
Proof.
move : sn_term_metric; repeat move/[apply].
move => [k]+.
eauto using term_metric_algo_dom.
Qed.