Nuprl Lemma : member-interface-predecessors2
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. ∀e':E(X). ((e' ∈ ≤(X)(e)) ⇒ e' ≤loc e )
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
es-interface-predecessors: ≤(X)(e),
eclass-events: eclass-events(es;X;L),
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E. \mforall{}e':E(X). ((e' \mmember{} \mleq{}(X)(e)) {}\mRightarrow{} e' \mleq{}loc e )
Date html generated:
2016_05_17-AM-06_59_24
Last ObjectModification:
2016_01_17-PM-06_44_13
Theory : event-ordering
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