Nuprl Lemma : fpf-dom_functionality2
∀[A:Type]. ∀[eq1,eq2:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[x:A].  {↑x ∈ dom(f) supposing ↑x ∈ dom(f)}
Proof
Definitions occuring in Statement : 
fpf-dom: x ∈ dom(f)
, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
assert: ↑b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
guard: {T}
, 
universe: Type
Definitions unfolded in proof : 
guard: {T}
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
prop: ℙ
, 
implies: P 
⇒ Q
Lemmas referenced : 
fpf-dom_functionality, 
top_wf, 
assert_wf, 
assert_witness, 
fpf-dom_wf, 
fpf_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
lambdaEquality, 
hypothesis, 
cumulativity, 
hypothesisEquality, 
hyp_replacement, 
equalitySymmetry, 
applyLambdaEquality, 
independent_functionElimination, 
isect_memberEquality, 
equalityTransitivity, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}[eq1,eq2:EqDecider(A)].  \mforall{}[f:a:A  fp->  Top].  \mforall{}[x:A].    \{\muparrow{}x  \mmember{}  dom(f)  supposing  \muparrow{}x  \mmember{}  dom(f)\}
Date html generated:
2018_05_21-PM-09_17_31
Last ObjectModification:
2018_02_09-AM-10_16_33
Theory : finite!partial!functions
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