Nuprl Lemma : es-prior-interface-val-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
prior(X)(e) = if pred(e) ∈b X then pred(e) else prior(X)(pred(e)) fi ∈ E supposing ↑e ∈b prior(X)
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-pred: pred(e),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
eclass_wf,
es-is-prior-interface-pred,
es-pred_wf,
bool_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-prior-interface-val,
es-locl-iff,
eclass-val_wf2,
es-prior-interface_wf,
es-E-interface_wf,
es-pred-locl,
decidable__es-locl,
assert_elim,
and_wf,
equal_wf,
not_assert_elim,
btrue_neq_bfalse,
es-locl_transitivity2,
es-le_weakening,
es-locl-total,
es-loc-pred
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
prior(X)(e) = if pred(e) \mmember{}\msubb{} X then pred(e) else prior(X)(pred(e)) fi supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2015_07_21-PM-02_47_11
Last ObjectModification:
2015_01_27-PM-07_39_04
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