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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