Nuprl Lemma : class-at-program_wf
∀[Info,B:Type]. ∀[X:EClass(B)]. ∀[pr:LocalClass(X)]. ∀[locs:bag(Id)].
(pr)@locs ∈ LocalClass(X@locs) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
class-at-program: (pr)@locs,
class-at: X@locs,
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
class-at-program: (pr)@locs,
all: ∀x:A. B[x],
class-at: X@locs,
class-ap: X(e),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
top: Top,
hdf-halt: hdf-halt(),
hdf-ap: X(a),
pi2: snd(t),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B)]. \mforall{}[pr:LocalClass(X)]. \mforall{}[locs:bag(Id)].
(pr)@locs \mmember{} LocalClass(X@locs) supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_08_59
Last ObjectModification:
2016_01_17-PM-09_12_11
Theory : local!classes
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