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Some definitions of interest.
append Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive)
Thm* T:Type, as,bs:T List. (as @ bs) T List
assert Def b == if b True else False fi
Thm* b:. b Prop
mapfilter Def mapfilter(f;P;L) == map(f;filter(P;L))
Thm* T:Type, P:(T), T':Type, f:({x:T| P(x) }T'), L:T List. mapfilter(f;P;L) T' List

About:
listconslist_indbool
ifthenelseassertsetapplyfunction
recursive_def_noticeuniversememberpropfalsetrueall
!abstraction

Definitions graph 1 1 Sections Graphs Doc