Nuprl Lemma : p-open-member_wf
∀[p:FinProbSpace]. ∀[C:p-open(p)]. ∀[s:ℕ ⟶ Outcome]. (s ∈ C ∈ ℙ)
Proof
Definitions occuring in Statement :
p-open-member: s ∈ C,
p-open: p-open(p),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
p-open-member: s ∈ C,
p-open: p-open(p),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
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,
all: ∀x:A. B[x],
int_seg: {i..j-}
Lemmas referenced :
finite-prob-space_wf,
le_wf,
all_wf,
set_wf,
subtype_rel_self,
false_wf,
int_seg_subtype_nat,
int_seg_wf,
p-outcome_wf,
subtype_rel_dep_function,
equal-wf-T-base,
nat_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
intEquality,
applyEquality,
setElimination,
rename,
hypothesisEquality,
dependent_pairEquality,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
because_Cache,
functionEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
productEquality
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[C:p-open(p)]. \mforall{}[s:\mBbbN{} {}\mrightarrow{} Outcome]. (s \mmember{} C \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-11_48_48
Last ObjectModification:
2016_01_17-AM-10_05_55
Theory : randomness
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