Nuprl Lemma : length_tl
∀[A:Type]. ∀[l:A List]. ||tl(l)|| = (||l|| - 1) ∈ ℤ supposing ||l|| ≥ 1
Proof
Definitions occuring in Statement :
length: ||as||,
tl: tl(l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
subtract: n - m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
subtract: n - m,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False,
cons: [a / b],
top: Top,
subtype_rel: A ⊆r B
Lemmas referenced :
ge_wf,
length_wf,
list_wf,
list-cases,
length_of_nil_lemma,
reduce_tl_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
reduce_tl_cons_lemma,
add-associates,
add-swap,
add-commutes,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
hypothesis,
extract_by_obid,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
because_Cache,
universeEquality,
dependent_functionElimination,
unionElimination,
productElimination,
independent_functionElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
voidEquality,
applyEquality,
lambdaEquality,
intEquality,
minusEquality,
addEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List]. ||tl(l)|| = (||l|| - 1) supposing ||l|| \mgeq{} 1
Date html generated:
2019_06_20-PM-00_40_04
Last ObjectModification:
2018_09_26-PM-02_12_31
Theory : list_0
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