Nuprl Lemma : es-prior-interface-equal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[e:E].
(prior(X)(e) = prior(Y)(e) ∈ E) supposing
((∀e':E. (((prior(X)(e) <loc e') ∨ (prior(Y)(e) <loc e')) ⇒ (e' <loc e) ⇒ (↑e' ∈b X ⇐⇒ ↑e' ∈b Y))) and
(↑e ∈b prior(X)) and
(↑e ∈b prior(Y)))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
all_wf,
or_wf,
es-locl_wf,
eclass-val_wf2,
es-prior-interface_wf,
es-E-interface_wf,
iff_wf,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
eclass_wf,
event-ordering+_wf,
es-prior-interface-val,
es-locl-total
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. \mforall{}[e:E].
(prior(X)(e) = prior(Y)(e)) supposing
((\mforall{}e':E
(((prior(X)(e) <loc e') \mvee{} (prior(Y)(e) <loc e'))
{}\mRightarrow{} (e' <loc e)
{}\mRightarrow{} (\muparrow{}e' \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e' \mmember{}\msubb{} Y))) and
(\muparrow{}e \mmember{}\msubb{} prior(X)) and
(\muparrow{}e \mmember{}\msubb{} prior(Y)))
Date html generated:
2015_07_21-PM-02_46_06
Last ObjectModification:
2015_01_27-PM-07_39_32
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