Theory: rec_type

Parents

• ltree

Type constants

Term constants

• TRP:('a -> 'a ltree list -> bool) -> 'a ltree -> bool {fixity = Prefix}

Axioms

Definitions

TRP_DEF

|- !P. TRP P = (@trp. !v tl. trp (Node v tl) = P v tl /\ EVERY trp tl)

Theorems

TRP

|- !P v tl. TRP P (Node v tl) = P v tl /\ EVERY (TRP P) tl

MAP_o

|- !f g. MAP (f o g) = MAP f o MAP g

TY_DEF_THM

|- !REP ABS P.
     (!a. ABS (REP a) = a) /\ (!r. TRP P r = REP (ABS r) = r) ==>
     (!f.
       ?!fn.
         !v tl.
           P v (MAP REP tl) ==>
           (fn (ABS (Node v (MAP REP tl))) = f (MAP fn tl) v tl))

exists_TRP

|- !P. (?v. P v []) ==> (?t. TRP P t)