Nuprl Lemma : continuous-monotone-co-value
ContinuousMonotone(T.atomic-values() ⋃ (T × T) ⋃ (T + T))
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(T.F[T]),
atomic-values: atomic-values(),
b-union: A ⋃ B,
product: x:A × B[x],
union: left + right
Definitions unfolded in proof :
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
not: ¬A,
implies: P ⇒ Q,
false: False,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
guard: {T},
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bor: p ∨bq,
bfalse: ff,
prop: ℙ,
cand: A c∧ B,
atomic-values: atomic-values(),
sq_stable: SqStable(P),
squash: ↓T,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
pi2: snd(t),
is-atomic: is-atomic(x)
Lemmas referenced :
subtype_rel_b-union,
atomic-values_wf,
b-union_wf,
subtype_rel_self,
subtype_rel_product,
subtype_rel_union,
subtype_rel_wf,
strong-continuous-b-union,
continuous-constant,
strong-continuous-product,
continuous-id,
strong-continuous-union,
isect2_wf,
subtype_rel_weakening,
nat_wf,
isect2_subtype_rel2,
testxxx_lemma,
equal_wf,
isect2_decomp,
isect2_subtype_rel,
false_wf,
sq_stable_from_decidable,
assert_wf,
is-atomic_wf,
decidable__assert,
sq_stable__all,
decidable__false
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productEquality,
cumulativity,
hypothesisEquality,
unionEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
lambdaEquality,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_functionElimination,
voidElimination,
isectEquality,
applyEquality,
functionExtensionality,
functionEquality,
instantiate,
rename,
unionElimination,
dependent_functionElimination,
voidEquality,
natural_numberEquality,
productElimination,
setElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityElimination
Latex:
ContinuousMonotone(T.atomic-values() \mcup{} (T \mtimes{} T) \mcup{} (T + T))
Date html generated:
2017_04_17-AM-09_07_25
Last ObjectModification:
2017_02_27-PM-05_15_00
Theory : rec_values
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