Nuprl Lemma : even-shorter-proof-of-termination-equality
∀[T:Type]. ∀[x,y:partial(T)]. 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,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
and: P ∧ Q,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
termination,
respects-equality-partial,
change-equality-type,
has-value_wf-partial,
partial_wf,
value-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
Error :productIsType,
Error :universeIsType,
Error :equalityIstype,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:partial(T)]. x = y supposing (x)\mdownarrow{} \mwedge{} (x = y) supposing value-type(T)
Date html generated:
2019_06_20-PM-00_33_58
Last ObjectModification:
2018_12_22-PM-01_16_48
Theory : partial_1
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