Nuprl Lemma : 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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
partial: partial(T),
quotient: x,y:A//B[x; y],
cand: A c∧ B,
value-type: value-type(T),
squash: ↓T,
true: True,
per-partial: per-partial(T;x;y),
uiff: uiff(P;Q)
Lemmas referenced :
termination,
equal_wf,
partial_wf,
inclusion-partial,
has-value_wf-partial,
value-type_wf,
equal-wf-base,
base-partial_wf,
per-partial_wf,
termination-equality-base,
value-type-has-value
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
lambdaFormation,
applyEquality,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
productEquality,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
pointwiseFunctionality,
independent_pairFormation,
lambdaEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:partial(T)]. x = y supposing (x)\mdownarrow{} \mwedge{} (x = y) supposing value-type(T)
Date html generated:
2018_05_21-PM-00_05_04
Last ObjectModification:
2018_05_19-AM-07_09_52
Theory : partial_1
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