Nuprl Lemma : es-prior-interface-same
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)].
(∀[e:E]. uiff(↑e ∈b prior(X);↑e ∈b prior(Y))) ∧ (∀[e:E]. prior(Y)(e) = prior(X)(e) ∈ E supposing ↑e ∈b prior(X))
supposing ∀e:E. (↑e ∈b X ⇐⇒ ↑e ∈b 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-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
is-prior-interface,
es-E-interface-property,
assert_wf,
in-eclass_wf,
es-locl_wf,
assert_witness,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
all_wf,
iff_wf,
es-prior-interface-equal,
or_wf,
eclass-val_wf2,
es-prior-interface_wf,
es-E-interface_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
(\mforall{}[e:E]. uiff(\muparrow{}e \mmember{}\msubb{} prior(X);\muparrow{}e \mmember{}\msubb{} prior(Y)))
\mwedge{} (\mforall{}[e:E]. prior(Y)(e) = prior(X)(e) supposing \muparrow{}e \mmember{}\msubb{} prior(X))
supposing \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} Y)
Date html generated:
2015_07_21-PM-02_46_18
Last ObjectModification:
2015_01_27-PM-07_37_38
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