Nuprl Lemma : not_all_sqequal
(∀[a,b:Base].  (a ~ b)) 
⇒ False
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
false: False
, 
base: Base
, 
sqequal: s ~ t
Definitions unfolded in proof : 
implies: P 
⇒ Q
, 
false: False
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
base_wf, 
uall_wf, 
not_zero_sqequal_one
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
baseClosed, 
lemma_by_obid, 
independent_functionElimination, 
voidElimination, 
sqequalRule, 
lambdaEquality, 
sqequalIntensionalEquality, 
hypothesisEquality
Latex:
(\mforall{}[a,b:Base].    (a  \msim{}  b))  {}\mRightarrow{}  False
Date html generated:
2016_05_13-PM-03_19_58
Last ObjectModification:
2016_01_14-PM-04_34_46
Theory : sqequal_1
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