Nuprl Lemma : es-interface-or-hasleft
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:EClass(Top)]. ∀[e:E]. oob-hasleft((A | B)(e)) ~ e ∈b A supposing ↑e ∈b (A | B)
Proof
Definitions occuring in Statement :
es-interface-or: (X | Y),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t,
oob-hasleft: oob-hasleft(x)
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-or: (X | Y),
eclass-val: X(e),
oob-apply: oob-apply(xs;ys),
eclass-compose2: eclass-compose2(f;X;Y),
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
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,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
top: Top,
assert: ↑b,
iff: P ⇐⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
oob-hasleft: oob-hasleft(x),
bor: p ∨bq,
oobleft?: oobleft?(x),
one_or_both_ind: one_or_both_ind(x;bval.both[bval];lval.left[lval];rval.right[rval]),
oobboth: oobboth(bval),
bfalse: ff,
oobboth?: oobboth?(x),
sq_type: SQType(T),
guard: {T},
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
false: False,
eq_int: (i =z j),
oobleft: oobleft(lval),
oobright: oobright(rval),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:EClass(Top)]. \mforall{}[e:E].
oob-hasleft((A | B)(e)) \msim{} e \mmember{}\msubb{} A supposing \muparrow{}e \mmember{}\msubb{} (A | B)
Date html generated:
2016_05_16-PM-10_43_24
Last ObjectModification:
2015_12_29-AM-10_53_51
Theory : event-ordering
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