Nuprl Lemma : fpf-ap_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. ∀[x:A]. f(x) ∈ B[x] supposing ↑x ∈ dom(f)
Proof
Definitions occuring in Statement :
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
pi2: snd(t),
pi1: fst(t),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x:A].
f(x) \mmember{} B[x] supposing \muparrow{}x \mmember{} dom(f)
Date html generated:
2016_05_16-AM-11_04_35
Last ObjectModification:
2015_12_29-AM-09_13_23
Theory : event-ordering
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