Nuprl Lemma : fpf-join-list_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[L:a:A fp-> B[a] List]. (⊕(L) ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf: a:A fp-> B[a],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-join-list: ⊕(L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
reduce_wf,
fpf_wf,
fpf-join_wf,
fpf-empty_wf,
list_wf,
deq_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,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[L:a:A fp-> B[a] List]. (\moplus{}(L) \mmember{} a:A fp-> B[a])
Date html generated:
2018_05_21-PM-09_22_37
Last ObjectModification:
2018_02_09-AM-10_18_49
Theory : finite!partial!functions
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