Nuprl Lemma : fpf-join-dom-da
∀f,g:x:Knd fp-> Type. ∀x:Knd. (↑x ∈ dom(f ⊕ g) ⇐⇒ (↑x ∈ dom(f)) ∨ (↑x ∈ dom(g)))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
Kind-deq: KindDeq,
Knd: Knd,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
rev_implies: P ⇐ Q,
or: P ∨ Q
Latex:
\mforall{}f,g:x:Knd fp-> Type. \mforall{}x:Knd. (\muparrow{}x \mmember{} dom(f \moplus{} g) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}x \mmember{} dom(f)) \mvee{} (\muparrow{}x \mmember{} dom(g)))
Date html generated:
2016_05_16-AM-11_31_04
Last ObjectModification:
2015_12_29-AM-09_26_46
Theory : event-ordering
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