Nuprl Lemma : prior-val-is
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[e:E]. ∀[e':E(X)].
({(↑e ∈b (X)') ∧ ((X)'(e) = X(e') ∈ T)}) supposing
((∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑e'' ∈b X))) and
(e' <loc e))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
es-E-interface: E(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],
guard: {T},
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
prior-val-val,
is-prior-val,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-locl_wf,
assert_wf,
assert_witness,
es-prior-val_wf,
top_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
all_wf,
not_wf,
es-E-interface_wf,
eclass_wf,
equal_wf,
eclass-val_wf,
and_wf,
member_wf,
es-locl-total,
not_assert_elim,
btrue_neq_bfalse
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[e:E]. \mforall{}[e':E(X)].
(\{(\muparrow{}e \mmember{}\msubb{} (X)') \mwedge{} ((X)'(e) = X(e'))\}) supposing
((\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X))) and
(e' <loc e))
Date html generated:
2015_07_21-PM-03_21_06
Last ObjectModification:
2015_01_27-PM-06_46_25
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