Nuprl Lemma : no-excluded-middle-quot-true
¬(∀P:ℙ. ⇃(P ∨ (↓¬P)))
Proof
Definitions occuring in Statement : 
quotient: x,y:A//B[x; y]
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
squash: ↓T
, 
or: P ∨ Q
, 
true: True
Definitions unfolded in proof : 
uimplies: b supposing a
, 
so_apply: x[s1;s2]
, 
so_lambda: λ2x y.t[x; y]
, 
or: P ∨ Q
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
has-value: (a)↓
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
and: P ∧ Q
, 
quotient: x,y:A//B[x; y]
, 
squash: ↓T
, 
top: Top
Lemmas referenced : 
equiv_rel_true, 
true_wf, 
not_wf, 
squash_wf, 
quotient_wf, 
sqle_wf_base, 
is-exception_wf, 
has-value_wf_base, 
exception-not-bottom, 
bottom_diverge, 
istype-sqle, 
bottom-sqle, 
not_id_sqeq_bottom, 
istype-void, 
member-not
Rules used in proof : 
independent_isectElimination, 
Error :unionIsType, 
Error :lambdaEquality_alt, 
cumulativity, 
unionEquality, 
Error :universeIsType, 
Error :functionIsType, 
dependent_functionElimination, 
equalitySymmetry, 
equalityTransitivity, 
Error :equalityIstype, 
Error :inhabitedIsType, 
universeEquality, 
hypothesisEquality, 
functionExtensionality, 
applyEquality, 
sqequalRule, 
because_Cache, 
baseClosed, 
isectElimination, 
voidElimination, 
hypothesis, 
thin, 
independent_functionElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
divergentSqle, 
sqleReflexivity, 
sqleRule, 
cut, 
rename, 
Error :lambdaFormation_alt, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
productElimination, 
promote_hyp, 
pertypeElimination, 
pointwiseFunctionalityForEquality, 
Error :productIsType, 
sqequalBase, 
unionElimination, 
imageElimination, 
sqequalSqle, 
Error :isect_memberEquality_alt
Latex:
\mneg{}(\mforall{}P:\mBbbP{}.  \00D9(P  \mvee{}  (\mdownarrow{}\mneg{}P)))
Date html generated:
2019_06_20-PM-00_32_43
Last ObjectModification:
2018_11_29-PM-04_55_48
Theory : quot_1
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