Nuprl Lemma : mkfpf_wf
∀[A:Type]. ∀[a:A List]. ∀[b:a:{a@0:A| (a@0 ∈ a)} ⟶ Top]. (mkfpf(a;b) ∈ a:A fp-> Top)
Proof
Definitions occuring in Statement :
mkfpf: mkfpf(a;b),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
mkfpf: mkfpf(a;b),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
l_member_wf,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[a:A List]. \mforall{}[b:a:\{a@0:A| (a@0 \mmember{} a)\} {}\mrightarrow{} Top]. (mkfpf(a;b) \mmember{} a:A fp-> Top)
Date html generated:
2018_05_21-PM-09_28_08
Last ObjectModification:
2018_02_09-AM-10_23_34
Theory : finite!partial!functions
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