Nuprl Lemma : inclusion-partial
∀[T:Type]. T ⊆r partial(T) supposing value-type(T)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
base-partial: base-partial(T),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
not: ¬A,
false: False,
true: True,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
partial: partial(T),
squash: ↓T,
has-value: (a)↓,
value-type: value-type(T),
uiff: uiff(P;Q),
per-partial: per-partial(T;x;y)
Lemmas referenced :
value-type_wf,
has-value_wf_base,
not_wf,
is-exception_wf,
istype-universe,
base_wf,
exception-not-value,
value-type-has-value,
member_wf,
squash_wf,
true_wf,
partial_wf,
quotient-member-eq,
per-partial-equiv_rel,
base-partial_wf,
per-partial_wf,
per-partial-reflex
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :isect_memberEquality_alt,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
Error :lambdaFormation_alt,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
Error :productIsType,
Error :isectIsType,
Error :equalityIsType4,
Error :inhabitedIsType,
independent_isectElimination,
independent_functionElimination,
voidElimination,
rename,
setElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
dependent_functionElimination,
lemma_by_obid,
imageElimination,
applyEquality,
pointwiseFunctionality,
lambdaEquality,
axiomSqleEquality,
isect_memberFormation
Latex:
\mforall{}[T:Type]. T \msubseteq{}r partial(T) supposing value-type(T)
Date html generated:
2019_06_20-PM-00_33_45
Last ObjectModification:
2018_10_06-PM-03_52_04
Theory : partial_1
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