Nuprl Lemma : inl-eta
∀[x:Top]. ∀d:Top + Top. d ~ inl outl(d) supposing d = (inl x) ∈ (Top + Top)
Proof
Definitions occuring in Statement : 
outl: outl(x)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
all: ∀x:A. B[x]
, 
inl: inl x
, 
union: left + right
, 
sqequal: s ~ t
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
outl: outl(x)
, 
sq_type: SQType(T)
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
true: True
, 
false: False
, 
prop: ℙ
Lemmas referenced : 
subtype_base_sq, 
int_subtype_base, 
equal_wf, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
unionElimination, 
thin, 
sqequalRule, 
sqequalHypSubstitution, 
applyEquality, 
lambdaEquality, 
natural_numberEquality, 
because_Cache, 
hypothesis, 
instantiate, 
lemma_by_obid, 
isectElimination, 
cumulativity, 
intEquality, 
independent_isectElimination, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
voidElimination, 
promote_hyp, 
sqequalAxiom, 
unionEquality, 
hypothesisEquality, 
inlEquality, 
isect_memberEquality
Latex:
\mforall{}[x:Top].  \mforall{}d:Top  +  Top.  d  \msim{}  inl  outl(d)  supposing  d  =  (inl  x)
Date html generated:
2016_05_13-PM-03_20_32
Last ObjectModification:
2015_12_26-AM-09_10_49
Theory : union
Home
Index