Nuprl Lemma : member-per-or-left
∀[A,B:Type]. ∀[a:A].  (<Ax, a> ∈ per-or(A;B))
Proof
Definitions occuring in Statement : 
per-or: per-or(A;B)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
pair: <a, b>
, 
universe: Type
, 
axiom: Ax
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
per-or: per-or(A;B)
, 
per-exists: per-exists(A;a.B[a])
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
per-or-family: per-or-family(A;B)
, 
has-value: (a)↓
, 
uimplies: b supposing a
Lemmas referenced : 
member-per-product, 
per-value_wf, 
per-or-family_wf, 
member-per-value, 
has-value_wf_base, 
is-exception_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
sqequalRule, 
hypothesisEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
universeEquality, 
sqleReflexivity, 
divergentSqle, 
independent_isectElimination, 
baseClosed, 
lemma_by_obid
Latex:
\mforall{}[A,B:Type].  \mforall{}[a:A].    (<Ax,  a>  \mmember{}  per-or(A;B))
Date html generated:
2019_06_20-AM-11_30_36
Last ObjectModification:
2018_08_22-PM-02_05_47
Theory : per!type
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