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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Latex:
\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:
2016_05_16-AM-10_43_32
Last ObjectModification:
2015_12_28-PM-07_41_25
Theory : halting!dataflow
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