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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