Nuprl Lemma : member-per-union-left
∀[A,B:Type]. ∀[x:A]. (inl x ∈ per-union(A;B))
Proof
Definitions occuring in Statement :
per-union: per-union(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
inl: inl x,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
per-union: per-union(A;B),
has-value: (a)↓,
outl: outl(x),
uimplies: b supposing a,
prop: ℙ,
true: True,
uand: uand(A;B),
top: Top,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
per-union_wf,
has-value_wf_base,
is-exception_wf,
uand_wf,
sqle_wf_base,
top_wf,
base_wf,
equal_wf,
squash_wf,
true_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
pointwiseFunctionality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
universeEquality,
extract_by_obid,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
baseClosed,
baseApply,
closedConclusion,
pertypeMemberEquality,
natural_numberEquality,
rename,
isaxiomCases,
axiomSqEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
instantiate
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A]. (inl x \mmember{} per-union(A;B))
Date html generated:
2019_06_20-AM-11_30_52
Last ObjectModification:
2018_08_07-PM-01_10_30
Theory : per!type
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