Nuprl Lemma : member-fpf-dom
∀[A:Type]. ∀eq:EqDecider(A). ∀f:a:A fp-> Top. ∀x:A. (↑x ∈ dom(f) ⇐⇒ (x ∈ fst(f)))
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
rev_implies: P ⇐ Q,
pi1: fst(t)
Latex:
\mforall{}[A:Type]. \mforall{}eq:EqDecider(A). \mforall{}f:a:A fp-> Top. \mforall{}x:A. (\muparrow{}x \mmember{} dom(f) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} fst(f)))
Date html generated:
2016_05_16-AM-11_32_57
Last ObjectModification:
2015_12_29-AM-09_28_17
Theory : event-ordering
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