Nuprl Lemma : fset-all_wf
∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[s:fset(T)]. (fset-all(s;x.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
fset-all: fset-all(s;x.P[x]),
fset: fset(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fset-all: fset-all(s;x.P[x]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
assert_wf,
fset-null_wf,
fset-filter_wf,
bnot_wf,
fset_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[s:fset(T)]. (fset-all(s;x.P[x]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_41_15
Last ObjectModification:
2015_12_26-PM-06_40_29
Theory : finite!sets
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