Nuprl Lemma : fpf-sub_witness
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> B[a]]. (f ⊆ g ⇒ (λx,y. <Ax, Ax> ∈ f ⊆ g))
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ─→ B[x],
pair: <a, b>,
universe: Type,
axiom: Ax
Lemmas :
assert_witness,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
assert_wf,
fpf-sub_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> B[a]]. (f \msubseteq{} g {}\mRightarrow{} (\mlambda{}x,y. <Ax, Ax> \mmember{} f \000C\msubseteq{} g))
Date html generated:
2015_07_17-AM-09_17_08
Last ObjectModification:
2015_01_28-AM-07_51_35
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