Nuprl Lemma : partial-partial
∀[A:Type]. (partial(partial(A)) ⊆r partial(A))
Proof
Definitions occuring in Statement :
partial: 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,
subtype_rel: A ⊆r B,
partial: partial(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
base-partial: base-partial(T),
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
per-partial: per-partial(T;x;y),
cand: A c∧ B,
uiff: uiff(P;Q),
label: ...$L... t
Lemmas referenced :
partial_wf,
quotient-member-eq,
base-partial_wf,
per-partial_wf,
per-partial-equiv_rel,
base-partial-partial,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
applyEquality,
setElimination,
rename,
Error :inhabitedIsType,
Error :universeIsType,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
Error :productIsType,
Error :equalityIsType4,
axiomEquality,
universeEquality,
independent_pairFormation,
promote_hyp
Latex:
\mforall{}[A:Type]. (partial(partial(A)) \msubseteq{}r partial(A))
Date html generated:
2019_06_20-PM-00_33_47
Last ObjectModification:
2018_10_06-PM-03_50_22
Theory : partial_1
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