Nuprl Lemma : hdf-bind-compose1-left
∀[A,B,C,U:Type]. ∀[f:B ─→ C]. ∀[X:hdataflow(A;B)]. ∀[Y:C ─→ hdataflow(A;U)].
(f o X >>= Y = X >>= Y o f ∈ hdataflow(A;U)) supposing (valueall-type(C) and valueall-type(U))
Proof
Definitions occuring in Statement :
hdf-bind: X >>= Y,
hdf-compose1: f o X,
hdataflow: hdataflow(A;B),
compose: f o g,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
hdf-bind-as-gen,
valueall-type_wf,
hdataflow_wf,
empty-bag_wf,
hdf-bind-gen_wf,
compose_wf,
hdf-bind-gen-compose1-left,
iff_weakening_equal
\mforall{}[A,B,C,U:Type]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:C {}\mrightarrow{} hdataflow(A;U)].
(f o X >>= Y = X >>= Y o f) supposing (valueall-type(C) and valueall-type(U))
Date html generated:
2015_07_17-AM-08_07_16
Last ObjectModification:
2015_02_03-PM-09_47_42
Home
Index