Nuprl Lemma : es-interface-predecessors-nonempty
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E(X)]. 0 < ||≤(X)(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),
length: ||as||,
less_than: a < b,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
or: P ∨ Q,
not: ¬A,
false: False,
cons: [a / b],
top: Top,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
guard: {T},
decidable: Dec(P),
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)]. 0 < ||\mleq{}(X)(e)||
Date html generated:
2016_05_16-PM-11_03_06
Last ObjectModification:
2016_01_17-PM-07_14_18
Theory : event-ordering
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