Nuprl Lemma : sequence-class-program_wf
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[Z:EClass(A)]. ∀[xpr:LocalClass(X)]. ∀[ypr:LocalClass(Y)].
∀[zpr:LocalClass(Z)].
sequence-class-program(xpr;ypr;zpr) ∈ LocalClass(sequence-class(X;Y;Z)) supposing valueall-type(A)
Proof
Definitions occuring in Statement :
sequence-class-program: sequence-class-program(xpr;ypr;zpr),
sequence-class: sequence-class(X;Y;Z),
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]},
sequence-class-program: sequence-class-program(xpr;ypr;zpr),
all: ∀x:A. B[x],
sequence-class: sequence-class(X;Y;Z),
class-ap: X(e),
member-eclass: e ∈b X,
squash: ↓T,
subtype_rel: A ⊆r B,
nat: ℕ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
Id: Id,
sq_type: SQType(T),
es-locl: (e <loc e'),
hdf-sequence: hdf-sequence(X;Y;Z),
not: ¬A,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
cons: [a / b],
colength: colength(L),
decidable: Dec(P),
nil: [],
less_than: a < b,
less_than': less_than'(a;b),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
ext-eq: A ≡ B,
pi1: fst(t),
bnot: ¬bb,
assert: ↑b,
hdf-run: hdf-run(P),
hdf-halt: hdf-halt(),
hdf-ap: X(a),
bag-null: bag-null(bs),
null: null(as),
pi2: snd(t),
empty-bag: {},
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
cand: A c∧ B,
iterate-hdataflow: P*(inputs),
list_accum: list_accum,
map: map(f;as),
list_ind: list_ind,
es-le: e ≤loc e' ,
es-le-before: ≤loc(e)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(A)]. \mforall{}[xpr:LocalClass(X)].
\mforall{}[ypr:LocalClass(Y)]. \mforall{}[zpr:LocalClass(Z)].
sequence-class-program(xpr;ypr;zpr) \mmember{} LocalClass(sequence-class(X;Y;Z)) supposing valueall-type(A)
Date html generated:
2016_05_17-AM-09_11_04
Last ObjectModification:
2016_01_17-PM-09_19_13
Theory : local!classes
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