Nuprl Lemma : interface-predecessors-tagged-true
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top × 𝔹)]. ∀[e:E]. (≤(Tagged_tt(X))(e) ~ filter(λe.(snd(X(e)));≤(X)(e)))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-tagged-true-class: Tagged_tt(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
filter: filter(P;l),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
lambda: λx.A[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
es-tagged-true-class: Tagged_tt(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-E-interface: E(X),
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ,
iff: P ⇐⇒ Q,
pi2: snd(t),
pi1: fst(t),
eq_int: (i =z j),
true: True,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top \mtimes{} \mBbbB{})]. \mforall{}[e:E].
(\mleq{}(Tagged\_tt(X))(e) \msim{} filter(\mlambda{}e.(snd(X(e)));\mleq{}(X)(e)))
Date html generated:
2016_05_17-AM-07_05_06
Last ObjectModification:
2016_01_17-PM-06_46_50
Theory : event-ordering
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