Nuprl Lemma : no-excluded-middle
¬(∀P:ℙ. (P ∨ (¬P)))
Proof
Definitions occuring in Statement : 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
or: P ∨ Q
Definitions unfolded in proof : 
not: ¬A
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
false: False
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
or: P ∨ Q
, 
so_apply: x[s]
, 
guard: {T}
Lemmas referenced : 
not_has-value_decidable_on_base, 
base_wf, 
all_wf, 
or_wf, 
not_wf, 
has-value_wf_base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
rename, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
independent_functionElimination, 
thin, 
hypothesis, 
voidElimination, 
instantiate, 
isectElimination, 
universeEquality, 
sqequalRule, 
lambdaEquality, 
cumulativity, 
hypothesisEquality, 
dependent_functionElimination
Latex:
\mneg{}(\mforall{}P:\mBbbP{}.  (P  \mvee{}  (\mneg{}P)))
Date html generated:
2016_05_13-PM-03_46_00
Last ObjectModification:
2015_12_26-AM-09_58_45
Theory : call!by!value_2
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