[ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair/
| #a #W0 #T0 #HT0 #HU
lapply (IHVs … HT0) -IHVs -HT0 #HT0
- elim (tstc_inv_bind_appls_simple … HT0) //
+ elim (tstc_inv_bind_applv_simple … HT0) //
| #a #V1 #V2 #V0 #T0 #HV1 #HV12 #HT0 #HU
lapply (IHVs … HT0) -IHVs -HT0 #HT0
- elim (tstc_inv_bind_appls_simple … HT0) //
+ elim (tstc_inv_bind_applv_simple … HT0) //
]
qed-.
[ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
| #a #W1 #T1 #HT1 #HU
elim (IHVs … HT1) -IHVs -HT1 #HT1
- [ elim (tstc_inv_bind_appls_simple … HT1) //
+ [ elim (tstc_inv_bind_applv_simple … HT1) //
| @or_intror (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV.ⓛ{a}W1.T1)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
]
| #a #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
elim (IHVs … HT1) -IHVs -HT1 #HT1
- [ elim (tstc_inv_bind_appls_simple … HT1) //
+ [ elim (tstc_inv_bind_applv_simple … HT1) //
| @or_intror (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV1.ⓓ{a}V3.T1)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
[ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
| #b #W1 #T1 #HT1 #HU
elim (IHVs … HT1) -IHVs -HT1 #HT1
- [ elim (tstc_inv_bind_appls_simple … HT1) //
+ [ elim (tstc_inv_bind_applv_simple … HT1) //
| @or_intror (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV0.ⓛ{b}W1.T1)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
]
| #b #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
elim (IHVs … HT1) -IHVs -HT1 #HT1
- [ elim (tstc_inv_bind_appls_simple … HT1) //
+ [ elim (tstc_inv_bind_applv_simple … HT1) //
| @or_intror (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV1.ⓓ{b}V3.T1)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
[ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
| #b #W0 #T0 #HT0 #HU
elim (IHVs … HT0) -IHVs -HT0 #HT0
- [ elim (tstc_inv_bind_appls_simple … HT0) //
+ [ elim (tstc_inv_bind_applv_simple … HT0) //
| @or_intror -i (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV.ⓛ{b}W0.T0)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
]
| #b #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
elim (IHVs … HT0) -IHVs -HT0 #HT0
- [ elim (tstc_inv_bind_appls_simple … HT0) //
+ [ elim (tstc_inv_bind_applv_simple … HT0) //
| @or_intror -i (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV0.ⓓ{b}V3.T0)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
elim (cpxs_inv_appl1 … H) -H *
[ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or3_intro0/
| #b #W0 #T0 #HT0 #HU elim (IHVs … HT0) -IHVs -HT0 #HT0
- [ elim (tstc_inv_bind_appls_simple … HT0) //
+ [ elim (tstc_inv_bind_applv_simple … HT0) //
| @or3_intro1 -W (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV.ⓛ{b}W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
]
| #b #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
elim (IHVs … HT0) -IHVs -HT0 #HT0
- [ elim (tstc_inv_bind_appls_simple … HT0) //
+ [ elim (tstc_inv_bind_applv_simple … HT0) //
| @or3_intro1 -W (**) (* explicit constructor *)
@(cpxs_trans … HU) -U
@(cpxs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/