X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flift_lift.ma;h=6aac2af44da004b28e098d83c20b2616304177b4;hb=2ba2dc23443ad764adab652e06d6f5ed10bd912d;hp=c0805dd87429f0370208f59a535acac9ea3f55a1;hpb=f16bbb93ecb40fa40f736e0b1158e1c7676a640a;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lift_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lift_lift.ma index c0805dd87..6aac2af44 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lift_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lift_lift.ma @@ -60,12 +60,12 @@ theorem lift_div_le: ∀d1,e1,T1,T. ⇧[d1, e1] T1 ≡ T → lapply (lift_inv_gref2 … Hk) -Hk #Hk destruct /3 width=3/ | #a #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 lapply (lift_inv_bind2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct - elim (IHW … HW2 ?) // -IHW -HW2 #W0 #HW2 #HW1 - >plus_plus_comm_23 in HU2; #HU2 elim (IHU … HU2 ?) /2 width=1/ /3 width=5/ + elim (IHW … HW2) // -IHW -HW2 #W0 #HW2 #HW1 + >plus_plus_comm_23 in HU2; #HU2 elim (IHU … HU2) /2 width=1/ /3 width=5/ | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 lapply (lift_inv_flat2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct - elim (IHW … HW2 ?) // -IHW -HW2 #W0 #HW2 #HW1 - elim (IHU … HU2 ?) // /3 width=5/ + elim (IHW … HW2) // -IHW -HW2 #W0 #HW2 #HW1 + elim (IHU … HU2) // /3 width=5/ ] qed. @@ -80,7 +80,7 @@ theorem lift_div_be: ∀d1,e1,T1,T. ⇧[d1, e1] T1 ≡ T → >(lift_inv_lref2_lt … H) -H [ /3 width=3/ | /2 width=3/ ] | #i #d1 #e1 #Hid1 #e #e2 #T2 #H #He1 #He1e2 elim (lt_or_ge (i+e1) (d1+e+e2)) #Hie1d1e2 - [ elim (lift_inv_lref2_be … H ? ?) -H // /2 width=1/ + [ elim (lift_inv_lref2_be … H) -H // /2 width=1/ | >(lift_inv_lref2_ge … H ?) -H // lapply (le_plus_to_minus … Hie1d1e2) #Hd1e21i elim (le_inv_plus_l … Hie1d1e2) -Hie1d1e2 #Hd1e12 #He2ie1 @@ -90,12 +90,12 @@ theorem lift_div_be: ∀d1,e1,T1,T. ⇧[d1, e1] T1 ≡ T → | #p #d1 #e1 #e #e2 #T2 #H >(lift_inv_gref2 … H) -H /2 width=3/ | #a #I #V1 #V #T1 #T #d1 #e1 #_ #_ #IHV1 #IHT1 #e #e2 #X #H #He1 #He1e2 elim (lift_inv_bind2 … H) -H #V2 #T2 #HV2 #HT2 #H destruct - elim (IHV1 … HV2 ? ?) -V // >plus_plus_comm_23 in HT2; #HT2 - elim (IHT1 … HT2 ? ?) -T // -He1 -He1e2 /3 width=5/ + elim (IHV1 … HV2) -V // >plus_plus_comm_23 in HT2; #HT2 + elim (IHT1 … HT2) -T // -He1 -He1e2 /3 width=5/ | #I #V1 #V #T1 #T #d1 #e1 #_ #_ #IHV1 #IHT1 #e #e2 #X #H #He1 #He1e2 elim (lift_inv_flat2 … H) -H #V2 #T2 #HV2 #HT2 #H destruct - elim (IHV1 … HV2 ? ?) -V // - elim (IHT1 … HT2 ? ?) -T // -He1 -He1e2 /3 width=5/ + elim (IHV1 … HV2) -V // + elim (IHT1 … HT2) -T // -He1 -He1e2 /3 width=5/ ] qed. @@ -162,12 +162,12 @@ theorem lift_trans_le: ∀d1,e1,T1,T. ⇧[d1, e1] T1 ≡ T → >(lift_inv_gref1 … HX) -HX /2 width=3/ | #a #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct - elim (IHV12 … HV20 ?) -IHV12 -HV20 // - elim (IHT12 … HT20 ?) -IHT12 -HT20 /2 width=1/ /3 width=5/ + elim (IHV12 … HV20) -IHV12 -HV20 // + elim (IHT12 … HT20) -IHT12 -HT20 /2 width=1/ /3 width=5/ | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct - elim (IHV12 … HV20 ?) -IHV12 -HV20 // - elim (IHT12 … HT20 ?) -IHT12 -HT20 // /3 width=5/ + elim (IHV12 … HV20) -IHV12 -HV20 // + elim (IHT12 … HT20) -IHT12 -HT20 // /3 width=5/ ] qed. @@ -189,13 +189,13 @@ theorem lift_trans_ge: ∀d1,e1,T1,T. ⇧[d1, e1] T1 ≡ T → >(lift_inv_gref1 … HX) -HX /2 width=3/ | #a #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hded elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct - elim (IHV12 … HV20 ?) -IHV12 -HV20 // - elim (IHT12 … HT20 ?) -IHT12 -HT20 /2 width=1/ #T + elim (IHV12 … HV20) -IHV12 -HV20 // + elim (IHT12 … HT20) -IHT12 -HT20 /2 width=1/ #T (lift_mono … H … HT1) -T // qed.