Nuprl Lemma : es-interface-val-restrict
∀[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ⟶ E ⟶ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E. Dec(P[es;e])]. ∀[es:EO+(Info)].
∀[e:E].
(I|p)(e) = I(e) ∈ A supposing ↑e ∈b (I|p)
Proof
Definitions occuring in Statement :
es-interface-restrict: (I|p),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
eclass-val: X(e),
es-interface-restrict: (I|p),
in-eclass: e ∈b X,
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
nat: ℕ,
uiff: uiff(P;Q),
eq_int: (i =z j),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
so_lambda: λ2x y.t[x; y]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[I:EClass(A)]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}[p:\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P[es;e])]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(I|p)(e) = I(e) supposing \muparrow{}e \mmember{}\msubb{} (I|p)
Date html generated:
2016_05_16-PM-10_47_07
Last ObjectModification:
2016_01_17-PM-07_19_21
Theory : event-ordering
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