Nuprl Lemma : es-interface-or-right-property
∀[Info,A:Type]. ∀[X:EClass(Top)]. ∀[Y:EClass(A)].
  es-interface-or-right((X | Y)) = Y ∈ EClass(A) supposing Singlevalued(Y)
Proof
Definitions occuring in Statement : 
es-interface-or-right: es-interface-or-right(X), 
es-interface-or: (X | Y), 
sv-class: Singlevalued(X), 
eclass: EClass(A[eo; e]), 
uimplies: b supposing a, 
uall: ∀[x:A]. B[x], 
top: Top, 
universe: Type, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x], 
member: t ∈ T, 
uimplies: b supposing a, 
eclass: EClass(A[eo; e]), 
es-interface-or: (X | Y), 
es-interface-or-right: es-interface-or-right(X), 
eclass-compose2: eclass-compose2(f;X;Y), 
oob-apply: oob-apply(xs;ys), 
es-filter-image: f[X], 
eclass-compose1: f o X, 
subtype_rel: A ⊆r B, 
all: ∀x:A. B[x], 
implies: P ⇒ Q, 
bool: 𝔹, 
unit: Unit, 
it: ⋅, 
btrue: tt, 
uiff: uiff(P;Q), 
and: P ∧ Q, 
nat: ℕ, 
ifthenelse: if b then t else f fi , 
top: Top, 
eq_int: (i =z j), 
cand: A c∧ B, 
decidable: Dec(P), 
or: P ∨ Q, 
satisfiable_int_formula: satisfiable_int_formula(fmla), 
exists: ∃x:A. B[x], 
false: False, 
not: ¬A, 
prop: ℙ, 
oob-getright?: oob-getright?(x), 
oob-getright: oob-getright(x), 
oob-hasright: oob-hasright(x), 
oobright?: oobright?(x), 
oobboth?: oobboth?(x), 
oobright-rval: oobright-rval(x), 
oobboth-bval: oobboth-bval(x), 
so_lambda: λ2x.t[x], 
so_apply: x[s], 
bor: p ∨bq, 
bfalse: ff, 
pi2: snd(t), 
sq_type: SQType(T), 
guard: {T}, 
bnot: ¬bb, 
assert: ↑b, 
sv-class: Singlevalued(X), 
nequal: a ≠ b ∈ T , 
le: A ≤ B, 
so_lambda: λ2x y.t[x; y], 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type].  \mforall{}[X:EClass(Top)].  \mforall{}[Y:EClass(A)].
    es-interface-or-right((X  |  Y))  =  Y  supposing  Singlevalued(Y)
Date html generated:
2016_05_16-PM-10_42_58
Last ObjectModification:
2016_01_17-PM-07_22_53
Theory : event-ordering
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