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
Home
Index