Notation init_hist := (Some (Tsh, [] : hist), Some ([] : hist)).

Lemma hist_R_valid : forall g R v, valid (hist_R g R) v = hist_R g R v.
Notation MA_witness g v R :=
(v, ghost init_hist g * R%function [] v, hist_R g R, ghost_hist Tsh ([] : hist) g).