Nuprl Lemma : fpf-sub_transitivity
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f,g,h:a:A fp-> B[a]]. (f ⊆ h) supposing (g ⊆ h and f ⊆ g)
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf-sub: f ⊆ g,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
prop: ℙ
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g,h:a:A fp-> B[a]].
(f \msubseteq{} h) supposing (g \msubseteq{} h and f \msubseteq{} g)
Date html generated:
2016_05_16-AM-11_07_01
Last ObjectModification:
2015_12_29-AM-09_15_16
Theory : event-ordering
Home
Index