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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