Nuprl Lemma : es-interface-val-conditional
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X,Y:EClass(A)]. ∀[e:E].
[X?Y](e) = if e ∈b X then X(e) else Y(e) fi ∈ A supposing ↑e ∈b [X?Y]
Proof
Definitions occuring in Statement :
cond-class: [X?Y],
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eclass-val: X(e),
in-eclass: e ∈b X,
cond-class: [X?Y],
eclass-compose2: eclass-compose2(f;X;Y),
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,
ifthenelse: if b then t else f fi ,
eclass: EClass(A[eo; e]),
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X,Y:EClass(A)]. \mforall{}[e:E].
[X?Y](e) = if e \mmember{}\msubb{} X then X(e) else Y(e) fi supposing \muparrow{}e \mmember{}\msubb{} [X?Y]
Date html generated:
2016_05_16-PM-10_33_44
Last ObjectModification:
2016_01_17-PM-07_24_54
Theory : event-ordering
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