Nuprl Lemma : es-interface-implies-decidable
∀[Info:Type]
∀es:EO+(Info). ∀A:Type. ∀X:EClass(A).
∃P:E ─→ A ─→ ℙ. ((∀e:E. Dec(∃a:A. P[e;a])) ∧ (∀e:E. ((↑e ∈b X ⇐⇒ ∃a:A. P[e;a]) ∧ P[e;X(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,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_witness,
in-eclass_wf,
exists_wf,
assert_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
eclass-val_wf,
decidable_functionality,
decidable__assert
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}A:Type. \mforall{}X:EClass(A).
\mexists{}P:E {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}
((\mforall{}e:E. Dec(\mexists{}a:A. P[e;a]))
\mwedge{} (\mforall{}e:E. ((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:A. P[e;a]) \mwedge{} P[e;X(e)] supposing \muparrow{}e \mmember{}\msubb{} X)))
Date html generated:
2015_07_17-PM-01_03_01
Last ObjectModification:
2015_01_27-PM-10_47_46
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