Nuprl Lemma : first-interface-implies-prior-interface
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)].
∀[e:E]. ↑e ∈b prior(Y) supposing ↑e ∈b prior(X) supposing ∀e:E. ((↑e ∈b X) ⇒ (¬↑e ∈b prior(X)) ⇒ (↑e ∈b Y))
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-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
assert_witness,
in-eclass_wf,
es-prior-interface_wf0,
assert_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
all_wf,
not_wf,
eclass_wf,
is-prior-interface,
decidable__assert,
es-E-interface-property,
es-locl_transitivity2,
es-le_weakening,
es-locl_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
\mforall{}[e:E]. \muparrow{}e \mmember{}\msubb{} prior(Y) supposing \muparrow{}e \mmember{}\msubb{} prior(X)
supposing \mforall{}e:E. ((\muparrow{}e \mmember{}\msubb{} X) {}\mRightarrow{} (\mneg{}\muparrow{}e \mmember{}\msubb{} prior(X)) {}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2015_07_21-PM-02_46_32
Last ObjectModification:
2015_01_27-PM-07_39_58
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