Nuprl Lemma : prior-val-val
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀e:E.
∃e':E
((e' <loc e) ∧ (↑e' ∈b X) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑e'' ∈b X))) ∧ ((X)'(e) = X(e') ∈ T))
supposing ↑e ∈b (X)'
Proof
Definitions occuring in Statement :
es-prior-val: (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],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_witness,
in-eclass_wf,
es-prior-val_wf,
top_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
is-prior-val,
assert_wf,
eclass_wf,
es-prior-interface_wf1,
subtype_top,
es-E-interface_wf,
bool_wf,
bag_only_single_lemma,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-prior-interface_wf,
es-prior-interface-val,
eclass-val_wf2,
es-locl_wf,
eclass-val_wf,
all_wf,
is-prior-interface
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}e:E.
\mexists{}e':E
((e' <loc e)
\mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X)))
\mwedge{} ((X)'(e) = X(e')))
supposing \muparrow{}e \mmember{}\msubb{} (X)'
Date html generated:
2015_07_21-PM-03_20_48
Last ObjectModification:
2015_01_27-PM-06_46_11
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