Nuprl Lemma : fpf-single_wf2
∀[A,B:Type]. ∀[x:A]. ∀[v:B]. ∀[eqa:EqDecider(A)]. (x : v ∈ a:A fp-> x : B(a)?Top)
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
fpf-single: x : v,
fpf-cap: f(x)?z,
all: ∀x:A. B[x],
top: Top,
fpf: a:A fp-> B[a],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
ifthenelse: if b then t else f fi ,
implies: P ⇒ Q,
bool: 𝔹
Lemmas referenced :
fpf-single_wf,
fpf_ap_pair_lemma,
ifthenelse_wf,
fpf-dom_wf,
cons_wf,
nil_wf,
l_member_wf,
top_wf,
equal_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
dependent_pairEquality,
functionExtensionality,
setEquality,
functionEquality,
universeEquality,
because_Cache,
applyEquality,
lambdaFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A]. \mforall{}[v:B]. \mforall{}[eqa:EqDecider(A)]. (x : v \mmember{} a:A fp-> x : B(a)?Top)
Date html generated:
2018_05_21-PM-09_24_27
Last ObjectModification:
2018_05_19-PM-04_36_55
Theory : finite!partial!functions
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