Nuprl Lemma : fpf-single_wf
∀[A:𝕌{j}]. ∀[B:A ⟶ Type]. ∀[x:A]. ∀[v:B[x]].  (x : v ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement : 
fpf-single: x : v
, 
fpf: a:A fp-> B[a]
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
fpf-single: x : v
, 
fpf: a:A fp-> B[a]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
Lemmas referenced : 
cons_wf, 
nil_wf, 
l_member_wf, 
member_singleton, 
subtype_rel_self, 
subtype_rel_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
dependent_pairEquality, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
because_Cache, 
hypothesis, 
lambdaEquality, 
lambdaFormation, 
setElimination, 
rename, 
dependent_functionElimination, 
productElimination, 
independent_functionElimination, 
applyEquality, 
equalitySymmetry, 
functionExtensionality, 
hyp_replacement, 
applyLambdaEquality, 
setEquality, 
functionEquality, 
universeEquality, 
axiomEquality, 
equalityTransitivity, 
isect_memberEquality
Latex:
\mforall{}[A:\mBbbU{}\{j\}].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[x:A].  \mforall{}[v:B[x]].    (x  :  v  \mmember{}  x:A  fp->  B[x])
Date html generated:
2018_05_21-PM-09_24_24
Last ObjectModification:
2018_02_09-AM-10_19_50
Theory : finite!partial!functions
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