include "lambda/paths/labeled_sequential_computation.ma".
include "lambda/paths/labeled_st_reduction.ma".
include "lambda/paths/labeled_sequential_computation.ma".
include "lambda/paths/labeled_st_reduction.ma".
(* PATH-LABELED STANDARD COMPUTATION (MULTISTEP) ****************************)
(* Note: lstar shuld be replaced by l_sreds *)
(* PATH-LABELED STANDARD COMPUTATION (MULTISTEP) ****************************)
(* Note: lstar shuld be replaced by l_sreds *)
lemma pl_sts_fwd_pl_sreds: ∀s,F1,F2. F1 Ⓡ↦*[s] F2 → ⇓F1 ↦*[s] ⇓F2.
#s #F1 #F2 #H @(lstar_ind_r … s F2 H) -s -F2 //
#p #s #F #F2 #_ #HF2 #IHF1
lemma pl_sts_fwd_pl_sreds: ∀s,F1,F2. F1 Ⓡ↦*[s] F2 → ⇓F1 ↦*[s] ⇓F2.
#s #F1 #F2 #H @(lstar_ind_r … s F2 H) -s -F2 //
#p #s #F #F2 #_ #HF2 #IHF1