Nuprl Lemma : bind-class-program_wf
∀[Info,A,B:Type].
∀[X:EClass(A)]. ∀[Y:A ⟶ EClass(B)]. ∀[xpr:LocalClass(X)]. ∀[ypr:a:A ⟶ LocalClass(Y[a])].
(xpr >>= ypr ∈ LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
bind-class-program: xpr >>= ypr,
bind-class: X >x> Y[x],
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
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]},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
bind-class-program: xpr >>= ypr,
class-ap: X(e),
bind-class: X >x> Y[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
false: False,
not: ¬A,
true: True,
es-info: info(e),
record-select: r.x,
eo-forward: eo.e,
eo-restrict: eo-restrict(eo;P),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
empty-bag: {},
simple-hdf-bind: simple-hdf-bind(X;Y),
single-bag: {x},
bag-append: as + bs,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-ap: X(a),
hdf-run: hdf-run(P),
simple-bind-nxt: simple-bind-nxt(Y; p; a),
pi1: fst(t),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi2: snd(t),
compose: f o g,
bag-filter: [x∈b|p[x]],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-le-before: ≤loc(e)
Latex:
\mforall{}[Info,A,B:Type].
\mforall{}[X:EClass(A)]. \mforall{}[Y:A {}\mrightarrow{} EClass(B)]. \mforall{}[xpr:LocalClass(X)]. \mforall{}[ypr:a:A {}\mrightarrow{} LocalClass(Y[a])].
(xpr >>= ypr \mmember{} LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_06_48
Last ObjectModification:
2016_01_17-PM-09_17_54
Theory : local!classes
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