Nuprl Lemma : length-is-colength
∀[t:Top]. (||t|| ~ colength(t))
Proof
Definitions occuring in Statement :
length: ||as||,
colength: colength(L),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
colength: colength(L),
length: ||as||,
list_ind: list_ind,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
fun_exp: f^n,
primrec: primrec(n;b;c),
top: Top,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+,
has-value: (a)↓
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
base_wf,
strictness-apply,
bottom-sqle,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
fun_exp_unroll_1,
istype-top,
has-value-implies-dec-ispair-2,
has-value_wf_base,
is-exception_wf,
bottom_diverge,
exception-not-bottom,
has-value-implies-dec-isaxiom-2,
top_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
sqequalSqle,
lambdaFormation,
fixpointLeast,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
isect_memberEquality,
voidEquality,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
intEquality,
minusEquality,
because_Cache,
dependent_set_memberEquality,
axiomSqEquality,
divergentSqle,
callbyvalueCallbyvalue,
callbyvalueReduce,
sqleRule,
baseApply,
closedConclusion,
baseClosed,
sqleReflexivity,
callbyvalueExceptionCases,
exceptionSqequal,
callbyvalueIsaxiom,
callbyvalueSpread,
equalityTransitivity,
equalitySymmetry,
productEquality,
isaxiomExceptionCases,
spreadExceptionCases
Latex:
\mforall{}[t:Top]. (||t|| \msim{} colength(t))
Date html generated:
2019_06_20-PM-00_39_57
Last ObjectModification:
2018_09_26-PM-02_59_09
Theory : list_0
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