Nuprl Lemma : eclass2-program_wf
∀[Info,B,C:Type].
∀[X:EClass(B ⟶ bag(C))]. ∀[Y:EClass(B)]. ∀[Xpr:LocalClass(X)]. ∀[Ypr:LocalClass(Y)].
(Xpr o Ypr ∈ LocalClass((X o Y)))
supposing valueall-type(C)
Proof
Definitions occuring in Statement :
eclass2-program: Xpr o Ypr,
eclass2: (X o 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,
function: x:A ⟶ B[x],
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]},
eclass2-program: Xpr o Ypr,
all: ∀x:A. B[x],
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],
eclass2: (X o Y),
class-ap: X(e),
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
ext-eq: A ≡ B,
hdf-compose2: X o 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 ,
bor: p ∨bq,
isr: isr(x),
bfalse: ff,
pi2: snd(t),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
btrue: tt,
pi1: fst(t)
Latex:
\mforall{}[Info,B,C:Type].
\mforall{}[X:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[Y:EClass(B)]. \mforall{}[Xpr:LocalClass(X)]. \mforall{}[Ypr:LocalClass(Y)].
(Xpr o Ypr \mmember{} LocalClass((X o Y)))
supposing valueall-type(C)
Date html generated:
2016_05_17-AM-09_04_49
Last ObjectModification:
2016_01_17-PM-09_17_24
Theory : local!classes
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