Nuprl Lemma : hdf-until-halt-right
∀[A,B:Type]. ∀[X:hdataflow(A;B)]. (hdf-until(X;hdf-halt()) = X ∈ hdataflow(A;B))
Proof
Definitions occuring in Statement :
hdf-until: hdf-until(X;Y),
hdf-halt: hdf-halt(),
hdataflow: hdataflow(A;B),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
cand: A c∧ B,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
hdf-until: hdf-until(X;Y),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
pi1: fst(t),
hdf-ap: X(a),
hdf-halt: hdf-halt(),
ifthenelse: if b then t else f fi ,
btrue: tt,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
bag-null: bag-null(bs),
null: null(as),
pi2: snd(t),
empty-bag: {},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ext-eq: A ≡ B,
hdf-run: hdf-run(P),
true: True
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B)]. (hdf-until(X;hdf-halt()) = X)
Date html generated:
2016_05_16-AM-10_41_22
Last ObjectModification:
2016_01_17-AM-11_13_25
Theory : halting!dataflow
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