Nuprl Lemma : decomp_wf
∀[F:Type ⟶ Type]. ∀[T:{T:Type| T ⊆r Base} ]. ∀[x:F[T]]. (decomp{i:l}(T.F[T];T;x) ∈ 𝕌')
Proof
Definitions occuring in Statement :
decomp: decomp{i:l}(S.F[S];T;x),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
decomp: decomp{i:l}(S.F[S];T;x),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
constructor_wf,
list_wf,
equal_wf,
ap-con_wf,
subtype_rel_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
universeEquality,
cumulativity,
hypothesis,
setEquality,
dependent_set_memberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[T:\{T:Type| T \msubseteq{}r Base\} ]. \mforall{}[x:F[T]]. (decomp\{i:l\}(T.F[T];T;x) \mmember{} \mBbbU{}')
Date html generated:
2018_05_21-PM-08_44_39
Last ObjectModification:
2017_07_26-PM-06_08_26
Theory : general
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