Nuprl Lemma : termination
∀[T:Type]. ∀[x:partial(T)]. x ∈ T supposing (x)↓ supposing value-type(T)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
partial: partial(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
label: ...$L... t,
guard: {T},
true: True,
per-partial: per-partial(T;x;y)
Lemmas referenced :
partial_wf,
value-type_wf,
istype-universe,
base-partial_wf,
per-partial_wf,
has-value-extensionality,
has-value_wf-partial,
has-value_wf_base,
member_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
Error :universeIsType,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
pointwiseFunctionalityForEquality,
sqequalRule,
pertypeElimination,
promote_hyp,
productElimination,
Error :productIsType,
Error :equalityIstype,
sqequalBase,
equalitySymmetry,
because_Cache,
isectEquality,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
hyp_replacement,
Error :dependent_set_memberEquality_alt,
equalityTransitivity,
Error :inhabitedIsType,
applyLambdaEquality,
setElimination,
rename,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
Error :isect_memberEquality_alt,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:partial(T)]. x \mmember{} T supposing (x)\mdownarrow{} supposing value-type(T)
Date html generated:
2019_06_20-PM-00_33_55
Last ObjectModification:
2018_11_29-PM-04_06_06
Theory : partial_1
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