Nuprl Lemma : termination-equality-base
∀[T:Type]. ∀[x,y:Base]. x = y ∈ T supposing (x)↓ ∧ (x = y ∈ partial(T)) 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],
and: P ∧ Q,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
and: P ∧ Q,
partial: partial(T),
quotient: x,y:A//B[x; y],
cand: A c∧ B,
label: ...$L... t,
guard: {T},
member: t ∈ T,
prop: ℙ,
per-partial: per-partial(T;x;y)
Lemmas referenced :
base-partial_wf,
per-partial_wf,
has-value_wf_base,
partial_wf,
istype-base,
value-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
hypothesis,
pertypeElimination,
promote_hyp,
Error :productIsType,
Error :equalityIstype,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalBase,
equalitySymmetry,
because_Cache,
instantiate,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:Base]. x = y supposing (x)\mdownarrow{} \mwedge{} (x = y) supposing value-type(T)
Date html generated:
2019_06_20-PM-00_33_53
Last ObjectModification:
2018_12_22-PM-01_07_43
Theory : partial_1
Home
Index