Nuprl Lemma : p-open_wf
∀[p:FinProbSpace]. (p-open(p) ∈ Type)
Proof
Definitions occuring in Statement :
p-open: p-open(p),
finite-prob-space: FinProbSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
p-open: p-open(p),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
int_seg: {i..j-},
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
int_seg_wf,
p-outcome_wf,
all_wf,
le_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_dep_function,
subtype_rel_self,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setEquality,
functionEquality,
productEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
lambdaEquality,
applyEquality,
dependent_pairEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:FinProbSpace]. (p-open(p) \mmember{} Type)
Date html generated:
2016_05_15-PM-11_48_43
Last ObjectModification:
2015_12_28-PM-07_14_46
Theory : randomness
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