qed-.
lemma sex_inv_tl (RN) (RP):
- â\88\80f,I1,I2,L1,L2. L1 ⪤[RN,RP,⫱f] L2 →
+ â\88\80f,I1,I2,L1,L2. L1 ⪤[RN,RP,â«°f] L2 →
RN L1 I1 I2 → RP L1 I1 I2 →
L1.ⓘ[I1] ⪤[RN,RP,f] L2.ⓘ[I2].
#RN #RP #f #I1 #I2 #L2 #L2 elim (pn_split f) *
lemma sex_fwd_bind (RN) (RP):
∀f,I1,I2,L1,L2.
- L1.â\93\98[I1] ⪤[RN,RP,f] L2.â\93\98[I2] â\86\92 L1 ⪤[RN,RP,⫱f] L2.
+ L1.â\93\98[I1] ⪤[RN,RP,f] L2.â\93\98[I2] â\86\92 L1 ⪤[RN,RP,â«°f] L2.
#RN #RP #f #I1 #I2 #L1 #L2 #Hf
elim (pn_split f) * #g #H destruct
[ elim (sex_inv_push … Hf) | elim (sex_inv_next … Hf) ] -Hf //
lapply (sex_inv_atom1 … H) -H #H destruct
| #f @or_intror #H
lapply (sex_inv_atom2 … H) -H #H destruct
-| #L2 #I2 #f elim (IH L2 (⫱f)) -IH #HL12
+| #L2 #I2 #f elim (IH L2 (â«°f)) -IH #HL12
[2: /4 width=3 by sex_fwd_bind, or_intror/ ]
elim (pn_split f) * #g #H destruct
[ elim (HRP L1 I1 I2) | elim (HRN L1 I1 I2) ] -HRP -HRN #HV12