Nuprl Lemma : es-is-prior-interface-pred
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. (↑e ∈b prior(X) ⇐⇒ (¬↑first(e)) ∧ ((↑pred(e) ∈b X) ∨ (↑pred(e) ∈b prior(X))))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type
Lemmas :
decidable__assert,
es-first_wf2,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
event-ordering+_wf,
es-pred_wf,
or_wf,
not_wf,
assert_witness,
es-prior-interface_wf0,
in-eclass_wf,
assert_wf,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
es-is-prior-interface,
iff_wf,
es-locl_wf,
exists_wf,
subtype_top,
es-interface-subtype_rel2,
equal_wf,
and_wf,
not_assert_elim,
es-locl-iff,
es-pred-locl,
es-le_weakening,
es-locl_transitivity2
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} prior(X) \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e)) \mwedge{} ((\muparrow{}pred(e) \mmember{}\msubb{} X) \mvee{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X))))
Date html generated:
2015_07_21-PM-02_44_54
Last ObjectModification:
2015_07_16-AM-09_42_11
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