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
Lemmas :
all_wf,
es-E_wf,
event-ordering+_subtype,
decidable_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
bag-size_wf,
nat_wf,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
equal-wf-T-base,
assert_of_eq_int,
assert_wf,
eq_int_wf,
member_wf,
bag_size_empty_lemma,
equal_wf,
in-eclass_wf,
es-interface-restrict_wf,
top_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
eclass_wf
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:
2015_07_20-PM-03_29_38
Last ObjectModification:
2015_01_27-PM-10_16_08
Home
Index