Nuprl Lemma : eclass-val_wf
∀[T:Type]. ∀[A:es:EO+(T) ⟶ E ⟶ Type]. ∀[X:EClass(A[es;e])]. ∀[eo:EO+(T)]. ∀[e:E]. X(e) ∈ A[eo;e] supposing ↑e ∈b X
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
implies: P ⇒ Q,
and: P ∧ Q,
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,
nat: ℕ,
uiff: uiff(P;Q)
Latex:
\mforall{}[T:Type]. \mforall{}[A:es:EO+(T) {}\mrightarrow{} E {}\mrightarrow{} Type]. \mforall{}[X:EClass(A[es;e])]. \mforall{}[eo:EO+(T)]. \mforall{}[e:E].
X(e) \mmember{} A[eo;e] supposing \muparrow{}e \mmember{}\msubb{} X
Date html generated:
2016_05_16-PM-02_19_12
Last ObjectModification:
2016_01_17-PM-07_35_05
Theory : event-ordering
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