Nuprl Lemma : classrel-classfun-res-alt1
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ X(e);if e ∈b X then v = X@e ∈ T else False fi ) supposing single-valued-classrel(es;X;T)
Proof
Definitions occuring in Statement :
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
not: ¬A,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} X(e);if e \mmember{}\msubb{} X then v = X@e else False fi ) supposing single-valued-classrel(es;X;T)
Date html generated:
2016_05_16-PM-01_45_08
Last ObjectModification:
2016_01_17-PM-07_48_21
Theory : event-ordering
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