Nuprl Lemma : es-interface-predecessors-equal-subtype
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)].
∀[e:E]. (≤(X)(e) = ≤(Y)(e) ∈ ({e':E(X)| loc(e') = loc(e) ∈ Id} List)) supposing ∀e:E. (↑e ∈b X ⇐⇒ ↑e ∈b Y)
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
\mforall{}[e:E]. (\mleq{}(X)(e) = \mleq{}(Y)(e)) supposing \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} Y)
Date html generated:
2016_05_17-AM-06_55_05
Last ObjectModification:
2015_12_29-AM-00_16_22
Theory : event-ordering
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