Nuprl Lemma : es-interface-conditional-domain
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X,Y:EClass(A)]. ∀[e:E]. e ∈b [X?Y] = e ∈b X ∨be ∈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,
bor: p ∨bq,
bool: 𝔹,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
in-eclass: e ∈b X,
cond-class: [X?Y],
eclass-compose2: eclass-compose2(f;X;Y),
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
bor: p ∨bq,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X,Y:EClass(A)]. \mforall{}[e:E]. e \mmember{}\msubb{} [X?Y] = e \mmember{}\msubb{} X \mvee{}\msubb{}e \mmember{}\msubb{} Y
Date html generated:
2016_05_16-PM-02_40_08
Last ObjectModification:
2015_12_29-AM-11_31_47
Theory : event-ordering
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