Nuprl Lemma : per-partial-equiv_rel
∀[T:Type]. EquivRel(base-partial(T);x,y.per-partial(T;x;y))
Proof
Definitions occuring in Statement :
per-partial: per-partial(T;x;y),
base-partial: base-partial(T),
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
per-partial: per-partial(T;x;y),
uiff: uiff(P;Q),
uimplies: b supposing a,
has-value: (a)↓,
prop: ℙ,
base-partial: base-partial(T),
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
per-partial-reflex,
base-partial_wf,
has-value_wf_base,
per-partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
axiomSqleEquality,
setElimination,
rename,
equalitySymmetry,
because_Cache,
equalityTransitivity,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. EquivRel(base-partial(T);x,y.per-partial(T;x;y))
Date html generated:
2016_05_14-AM-06_09_22
Last ObjectModification:
2015_12_26-AM-11_52_29
Theory : partial_1
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