Nuprl Lemma : unsquashed-weak-continuity-false2
¬(∀F:(ℕ ⟶ ℕ) ⟶ ℕ. ∀a:ℕ ⟶ ℕ.  ∃n:ℕ. ∀b:ℕ ⟶ ℕ. ((∀i:ℕn. ((a i) = (b i) ∈ ℕ)) 
⇒ ((F a) = (F b) ∈ ℕ)))
Proof
Definitions occuring in Statement : 
int_seg: {i..j-}
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
not: ¬A
, 
implies: P 
⇒ Q
, 
unsquashed-WCP: unsquashed-WCP
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
le: A ≤ B
, 
and: P ∧ Q
, 
less_than': less_than'(a;b)
, 
false: False
, 
so_apply: x[s]
, 
nat: ℕ
, 
pi1: fst(t)
Lemmas referenced : 
unsquashed-weak-continuity-false, 
all_wf, 
nat_wf, 
int_seg_wf, 
equal_wf, 
int_seg_subtype_nat, 
false_wf, 
exists_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
independent_functionElimination, 
thin, 
hypothesis, 
dependent_functionElimination, 
hypothesisEquality, 
promote_hyp, 
productElimination, 
dependent_pairFormation, 
isectElimination, 
functionEquality, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
natural_numberEquality, 
applyEquality, 
functionExtensionality, 
independent_isectElimination, 
independent_pairFormation, 
voidElimination, 
setElimination, 
rename, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mneg{}(\mforall{}F:(\mBbbN{}  {}\mrightarrow{}  \mBbbN{})  {}\mrightarrow{}  \mBbbN{}.  \mforall{}a:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}.    \mexists{}n:\mBbbN{}.  \mforall{}b:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}.  ((\mforall{}i:\mBbbN{}n.  ((a  i)  =  (b  i)))  {}\mRightarrow{}  ((F  a)  =  (F  b))))
Date html generated:
2017_04_17-AM-09_41_08
Last ObjectModification:
2017_02_27-PM-05_36_00
Theory : fan-theorem
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