Nuprl Lemma : not-poly-choice-eta-2'
¬(∀f:Base. ((∀x,y:Base.  ((f x y) = x ∈ Base)) 
⇒ (f ~ λx,y. x)))
Proof
Definitions occuring in Statement : 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
apply: f a
, 
lambda: λx.A[x]
, 
base: Base
, 
sqequal: s ~ t
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
not: ¬A
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
false: False
Lemmas referenced : 
not-poly-choice-eta-2, 
all_wf, 
base_wf, 
equal-wf-base, 
sqequal-wf-base
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
independent_functionElimination, 
thin, 
hypothesis, 
dependent_functionElimination, 
hypothesisEquality, 
sqequalRule, 
isectElimination, 
lambdaEquality, 
baseApply, 
closedConclusion, 
baseClosed, 
voidElimination, 
functionEquality
Latex:
\mneg{}(\mforall{}f:Base.  ((\mforall{}x,y:Base.    ((f  x  y)  =  x))  {}\mRightarrow{}  (f  \msim{}  \mlambda{}x,y.  x)))
Date html generated:
2018_05_21-PM-01_15_34
Last ObjectModification:
2018_05_02-PM-01_18_57
Theory : num_thy_1
Home
Index