Nuprl Lemma : parallel-class-program_wf
∀[Info,B:Type].
∀[X,Y:EClass(B)]. ∀[Xpr:LocalClass(X)]. ∀[Ypr:LocalClass(Y)]. (Xpr || Ypr ∈ LocalClass(X || Y))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
parallel-class: X || Y,
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
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]},
parallel-class-program: X || Y,
all: ∀x:A. B[x],
parallel-class: X || Y,
class-ap: X(e),
eclass-compose2: eclass-compose2(f;X;Y),
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
ext-eq: A ≡ B,
hdf-parallel: X || Y,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-halted: hdf-halted(P),
hdf-ap: X(a),
hdf-run: hdf-run(P),
hdf-halt: hdf-halt(),
ifthenelse: if b then t else f fi ,
band: p ∧b q,
isr: isr(x),
bfalse: ff,
pi2: snd(t),
btrue: tt,
pi1: fst(t),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
unit: Unit
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X,Y:EClass(B)]. \mforall{}[Xpr:LocalClass(X)]. \mforall{}[Ypr:LocalClass(Y)]. (Xpr || Ypr \mmember{} LocalClass(X || Y))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_08_40
Last ObjectModification:
2016_01_17-PM-09_14_30
Theory : local!classes
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