Nuprl Lemma : loop-class-memory-program_wf
∀[Info,B:Type].
∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[pr:LocalClass(X)].
(loop-class-memory-program(pr;init) ∈ LocalClass(loop-class-memory(X;init)))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
loop-class-memory-program: loop-class-memory-program(pr;init),
loop-class-memory: loop-class-memory(X;init),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
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]},
loop-class-memory-program: loop-class-memory-program(pr;init),
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],
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,
top: Top,
and: P ∧ Q,
guard: {T},
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,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
es-before: before(e),
bfalse: ff,
true: True,
eclass3: eclass3(X;Y),
class-ap: X(e),
hdf-memory: hdf-memory(X;bs),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-ap: X(a),
hdf-run: hdf-run(P),
Id: Id,
es-E: E,
es-base-E: es-base-E(es),
sq_type: SQType(T),
ext-eq: A ≡ B,
pi1: fst(t),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
empty-bag: {},
nil: [],
has-value: (a)↓,
has-valueall: has-valueall(a),
bnot: ¬bb,
assert: ↑b,
pi2: snd(t),
member-eclass: e ∈b X,
bag-null: bag-null(bs),
hdf-halt: hdf-halt(),
eq_int: (i =z j),
eclass: EClass(A[eo; e])
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[pr:LocalClass(X)].
(loop-class-memory-program(pr;init) \mmember{} LocalClass(loop-class-memory(X;init)))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_07_51
Last ObjectModification:
2016_01_17-PM-09_15_48
Theory : local!classes
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