Nuprl Lemma : not_has-value_decidable_on_base_quot_true
¬(∀t:Base. ⇃((t)↓ ∨ (¬(t)↓)))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
has-value: (a)↓,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
true: True,
base: Base
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
false: False,
so_apply: x[s1;s2],
uimplies: b supposing a,
has-value: (a)↓,
subtype_rel: A ⊆r B,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
true: True
Lemmas referenced :
istype-base,
quotient_wf,
has-value_wf_base,
not_wf,
true_wf,
istype-void,
equiv_rel_true,
bottom_diverge,
exception-not-bottom,
is-exception_wf,
not-id-sqle-bottom,
base_wf,
or-quotient-true-subtype,
false_wf,
istype-sqle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
rename,
sqequalRule,
Error :functionIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :universeIsType,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
Error :unionIsType,
because_Cache,
independent_isectElimination,
sqleRule,
sqleReflexivity,
divergentSqle,
independent_functionElimination,
voidElimination,
baseClosed,
applyEquality,
functionExtensionality,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
pointwiseFunctionalityForEquality,
pertypeElimination,
promote_hyp,
productElimination,
natural_numberEquality,
Error :productIsType,
sqequalBase
Latex:
\mneg{}(\mforall{}t:Base. \00D9((t)\mdownarrow{} \mvee{} (\mneg{}(t)\mdownarrow{})))
Date html generated:
2019_06_20-PM-00_33_02
Last ObjectModification:
2018_11_28-AM-11_22_03
Theory : quot_1
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