Nuprl Lemma : until-class-program_wf
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[Y:EClass(C)]. ∀[xpr:LocalClass(X)]. ∀[ypr:LocalClass(Y)].
(until-class-program(xpr;ypr) ∈ LocalClass((X until Y)))
Proof
Definitions occuring in Statement :
until-class-program: until-class-program(xpr;ypr),
until-class: (X until Y),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
until-class-program: until-class-program(xpr;ypr),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
guard: {T},
and: P ∧ Q,
class-pred: class-pred(X;es;e),
class-ap: X(e),
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-before: before(e),
es-local-pred: last(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
isl: isl(x),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
pi1: fst(t),
ext-eq: A ≡ B,
hdf-run: hdf-run(P),
hdf-halt: hdf-halt(),
pi2: snd(t),
bag-null: bag-null(bs),
null: null(as),
hdf-ap: X(a),
empty-bag: {},
nil: [],
true: True,
until-class: (X until Y),
es-loc: loc(e),
es-info: info(e),
map: map(f;as),
iterate-hdataflow: P*(inputs),
hdf-until: hdf-until(X;Y),
hdf-halted: hdf-halted(P),
record-select: r.x,
es-first: first(e),
es-pred: pred(e),
cons: [a / b],
append: as @ bs,
list_ind: list_ind,
list_accum: list_accum,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
isr: isr(x),
bottom: ⊥,
es-eq-E: e = e',
es-dom: es-dom(es),
bor: p ∨bq,
es-base-pred: pred1(e),
es-eq: es-eq(es),
let: let,
eq_id: a = b,
es-locless: es-locless(es;e1;e2),
band: p ∧b q,
id-deq: IdDeq,
infix_ap: x f y,
atom2-deq: Atom2Deq,
eq_atom: eq_atom$n(x;y)
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[Y:EClass(C)]. \mforall{}[xpr:LocalClass(X)]. \mforall{}[ypr:LocalClass(Y)].
(until-class-program(xpr;ypr) \mmember{} LocalClass((X until Y)))
Date html generated:
2016_05_17-AM-09_05_50
Last ObjectModification:
2016_01_17-PM-09_17_18
Theory : local!classes
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