Nuprl Lemma : length-if-co-list-sq
∀[T:Type]. ∀[t:colist(T)]. ∀[n:ℕ]. ||t|| ~ n supposing ||t|| = n ∈ partial(ℤ)
Proof
Definitions occuring in Statement :
length: ||as||,
colist: colist(T),
partial: partial(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
length-in-bar-int-if-co-list,
subtype_base_sq,
int_subtype_base,
equal_wf,
partial_wf,
subtype_rel_set,
le_wf,
inclusion-partial,
int-value-type,
nat_wf,
colist_wf,
termination-equality,
value-type-has-value,
set-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
applyEquality,
sqequalRule,
because_Cache,
lambdaEquality,
natural_numberEquality,
universeEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. \mforall{}[n:\mBbbN{}]. ||t|| \msim{} n supposing ||t|| = n
Date html generated:
2016_05_15-PM-10_10_12
Last ObjectModification:
2015_12_27-PM-05_59_03
Theory : eval!all
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