Nuprl Lemma : base-partial-partial
∀[A:Type]. (base-partial(partial(A)) ⊆r base-partial(A))
Proof
Definitions occuring in Statement :
partial: partial(T),
base-partial: base-partial(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
base-partial: base-partial(T),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
partial: partial(T),
quotient: x,y:A//B[x; y],
per-partial: per-partial(T;x;y)
Lemmas referenced :
subtype_rel_sets,
base_wf,
has-value_wf_base,
equal-wf-base,
not_wf,
is-exception_wf,
partial_wf,
base-partial_wf,
per-partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
Error :lambdaEquality_alt,
productEquality,
isectEquality,
hypothesisEquality,
Error :universeIsType,
independent_isectElimination,
setElimination,
rename,
Error :setIsType,
Error :productIsType,
Error :isectIsType,
Error :equalityIsType4,
Error :lambdaFormation_alt,
productElimination,
independent_pairFormation,
pertypeElimination,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A:Type]. (base-partial(partial(A)) \msubseteq{}r base-partial(A))
Date html generated:
2019_06_20-PM-00_33_46
Last ObjectModification:
2018_10_06-PM-04_18_29
Theory : partial_1
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