Nuprl Lemma : es-interface-or-left-property
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(Top)].
es-interface-or-left((X | Y)) = X ∈ EClass(A) supposing Singlevalued(X)
Proof
Definitions occuring in Statement :
es-interface-or-left: es-interface-or-left(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-left: es-interface-or-left(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-getleft?: oob-getleft?(x),
oob-getleft: oob-getleft(x),
oob-hasleft: oob-hasleft(x),
oobleft?: oobleft?(x),
oobboth?: oobboth?(x),
oobleft-lval: oobleft-lval(x),
oobboth-bval: oobboth-bval(x),
so_lambda: λ2x.t[x],
so_apply: x[s],
bor: p ∨bq,
bfalse: ff,
pi1: fst(t),
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
sv-class: Singlevalued(X),
le: A ≤ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(Top)].
es-interface-or-left((X | Y)) = X supposing Singlevalued(X)
Date html generated:
2016_05_16-PM-10_42_17
Last ObjectModification:
2016_01_17-PM-07_22_35
Theory : event-ordering
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