Nuprl Lemma : not-poly-choice-eta-2
¬(∀f:Base. ((∀x,y:Base. ((f x y) = x ∈ Base)) ⇒ (f ~ λx,y. (f x y))))
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 :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
has-value: (a)↓,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
false: False
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
base_wf,
all_wf,
equal-wf-base,
sqequal-wf-base,
cbv_bottom_lemma,
not-btrue-sqle-bottom,
strictness-islambda,
bottom-sqle
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalSqle,
divergentSqle,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
hypothesis,
callbyvalueApply,
callbyvalueCallbyvalue,
callbyvalueReduce,
sqleReflexivity,
applyExceptionCases,
axiomSqleEquality,
callbyvalueExceptionCases,
exceptionSqequal,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
lambdaEquality,
functionEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mneg{}(\mforall{}f:Base. ((\mforall{}x,y:Base. ((f x y) = x)) {}\mRightarrow{} (f \msim{} \mlambda{}x,y. (f x y))))
Date html generated:
2018_05_21-PM-01_15_30
Last ObjectModification:
2018_05_01-PM-04_37_49
Theory : num_thy_1
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