Nuprl Lemma : es-interface-set-subtype
∀[Info,A:Type]. ∀[P:A ⟶ ℙ]. ∀[X:EClass(A)].
(X ∈ EClass({a:A| P[a]} )) supposing ((∀es:EO+(Info). ∀e:E(X). P[X(e)]) and Singlevalued(X))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
sv-class: Singlevalued(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
so_apply: x[s],
es-E-interface: E(X),
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
sv-class: Singlevalued(X),
decidable: Dec(P),
or: P ∨ Q,
eclass-val: X(e),
in-eclass: e ∈b X,
and: P ∧ Q,
cand: A c∧ B,
nat: ℕ,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T ,
ge: i ≥ j
Latex:
\mforall{}[Info,A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:EClass(A)].
(X \mmember{} EClass(\{a:A| P[a]\} )) supposing ((\mforall{}es:EO+(Info). \mforall{}e:E(X). P[X(e)]) and Singlevalued(X))
Date html generated:
2016_05_16-PM-10_23_31
Last ObjectModification:
2016_01_17-PM-07_31_56
Theory : event-ordering
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