Nuprl Lemma : fpf-join-dom-decl
∀f,g:x:Id fp-> Type. ∀x:Id. (↑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],
id-deq: IdDeq,
Id: Id,
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:Id fp-> Type. \mforall{}x:Id. (\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_30_58
Last ObjectModification:
2015_12_29-AM-09_26_40
Theory : event-ordering
Home
Index