Nuprl Lemma : co-value-height_wf
∀[t:co-value()]. (co-value-height(t) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
co-value-height: co-value-height(t),
co-value: co-value(),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
co-value: co-value(),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
co-value-height: co-value-height(t),
atomic-values: atomic-values(),
Value: Value(),
has-value: (a)↓,
top: Top,
is-atomic: is-atomic(x),
assert: ↑b,
bfalse: ff,
false: False,
outl: outl(x),
outr: outr(x),
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
fix_wf_corec-partial1,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
nat-mono,
b-union_wf,
atomic-values_wf,
istype-universe,
continuous-monotone-co-value,
partial_wf,
co-value_wf,
has-value_wf_base,
is-exception_wf,
istype-top,
istype-void,
nat-partial-nat,
istype-false,
istype-le,
add-wf-partial-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
Error :lambdaEquality_alt,
closedConclusion,
natural_numberEquality,
hypothesisEquality,
productEquality,
because_Cache,
unionEquality,
instantiate,
universeEquality,
Error :isect_memberEquality_alt,
imageElimination,
productElimination,
unionElimination,
equalityElimination,
Error :universeIsType,
Error :functionIsType,
applyEquality,
setElimination,
rename,
ispairCases,
divergentSqle,
baseClosed,
axiomSqEquality,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
voidElimination,
isinlCases,
isinrCases,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
Error :lambdaFormation_alt
Latex:
\mforall{}[t:co-value()]. (co-value-height(t) \mmember{} partial(\mBbbN{}))
Date html generated:
2019_06_20-PM-01_54_19
Last ObjectModification:
2018_10_17-PM-00_31_48
Theory : rec_values
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