Nuprl Lemma : assert-fpf-is-empty
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:x:A fp-> B[x]]. uiff(↑fpf-is-empty(f);f = ⊗ ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-is-empty: fpf-is-empty(f),
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
fpf: a:A fp-> B[a],
fpf-is-empty: fpf-is-empty(f),
pi1: fst(t),
fpf-empty: ⊗,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
top: Top,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
not: ¬A,
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. uiff(\muparrow{}fpf-is-empty(f);f = \motimes{})
Date html generated:
2016_05_16-AM-11_04_24
Last ObjectModification:
2015_12_29-AM-09_13_39
Theory : event-ordering
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