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Prove some simple impossible cases

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Yiyun Liu 2025-02-26 19:46:00 -05:00
parent f8943e3a9c
commit af0cac15e6
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theories/fp_red.v
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@ -2038,6 +2038,13 @@ Module EReds.
- hauto lq:on rew:off ctrs:rtc, ERed.R inv:ERed.R, rtc.
Qed.
Lemma zero_inv n (C : PTm n) :
rtc ERed.R PZero C -> C = PZero.
move E : PZero => u hu.
move : E. elim : u C /hu=>//=.
- hauto lq:on rew:off ctrs:rtc, ERed.R inv:ERed.R, rtc.
Qed.
Lemma ind_inv n P (a : PTm n) b c C :
rtc ERed.R (PInd P a b c) C ->
exists P0 a0 b0 c0, rtc ERed.R P P0 /\ rtc ERed.R a a0 /\
@ -2410,6 +2417,13 @@ Module REReds.
induction h; hauto lq:on rew:off ctrs:rtc use:RERed.ToBetaEta, RReds.nf_refl, @rtc_once, ERed.nf_preservation.
Qed.
Lemma zero_inv n (C : PTm n) :
rtc RERed.R PZero C -> C = PZero.
move E : PZero => u hu.
move : E. elim : u C /hu=>//=.
- hauto lq:on rew:off ctrs:rtc, RERed.R inv:RERed.R, rtc.
Qed.
Lemma suc_inv n (a : PTm n) C :
rtc RERed.R (PSuc a) C ->
exists b, rtc RERed.R a b /\ C = PSuc b.
@ -2421,6 +2435,15 @@ Module REReds.
- hauto lq:on rew:off ctrs:rtc, RERed.R inv:RERed.R, rtc.
Qed.
Lemma nat_inv n C :
rtc RERed.R (@PNat n) C ->
C = PNat.
Proof.
move E : PNat => u hu. move : E.
elim : u C / hu=>//=.
hauto lq:on rew:off ctrs:rtc, RERed.R inv:RERed.R.
Qed.
End REReds.
Module LoRed.