Nuprl Lemma : fs-predicate_wf
∀[K:RngSig]. ∀[S:Type]. ∀[P:(|K| × S) ⟶ ℙ]. ∀[f:formal-sum(K;S)]. (fs-predicate(K;S;p.P[p];f) ∈ ℙ)
Proof
Definitions occuring in Statement :
fs-predicate: fs-predicate(K;S;p.P[p];f),
formal-sum: formal-sum(K;S),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fs-predicate: fs-predicate(K;S;p.P[p];f),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
formal-sum: formal-sum(K;S),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
so_apply: x[s]
Lemmas referenced :
squash_wf,
exists_wf,
basic-formal-sum_wf,
equal_wf,
formal-sum_wf,
subtype_quotient,
bfs-equiv_wf,
bfs-equiv-rel,
bfs-predicate_wf,
rng_car_wf,
istype-universe,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
productEquality,
because_Cache,
applyEquality,
inhabitedIsType,
independent_isectElimination,
dependent_functionElimination,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
functionIsType,
productIsType,
universeEquality,
instantiate
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[P:(|K| \mtimes{} S) {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:formal-sum(K;S)]. (fs-predicate(K;S;p.P[p];f) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_29_00
Last ObjectModification:
2019_08_19-AM-10_52_24
Theory : linear!algebra
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