Nuprl Lemma : es-interface-conditional-domain-iff
∀[Info:Type]. ∀es:EO+(Info). ∀[A:Type]. ∀X,Y:EClass(A). ∀e:E. (↑e ∈b [X?Y] ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
cond-class: [X?Y],
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
uimplies: b supposing a,
top: Top,
guard: {T},
uiff: uiff(P;Q),
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
implies: P ⇒ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}[A:Type]. \mforall{}X,Y:EClass(A). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} [X?Y] \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X) \mvee{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_16-PM-02_40_23
Last ObjectModification:
2015_12_29-AM-11_31_35
Theory : event-ordering
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