Nuprl Lemma : length-zero-implies-sq-nil
∀l:Top List. l ~ [] supposing ||l|| = 0 ∈ ℤ
Proof
Definitions occuring in Statement :
length: ||as||,
nil: [],
list: T List,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
cons: [a / b],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ
Lemmas referenced :
list_wf,
length_wf,
equal_wf,
int_formula_prop_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
non_neg_length,
length_of_cons_lemma,
product_subtype_list,
length_of_nil_lemma,
list-cases,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
sqequalAxiom
Latex:
\mforall{}l:Top List. l \msim{} [] supposing ||l|| = 0
Date html generated:
2016_05_14-PM-02_57_55
Last ObjectModification:
2016_01_15-AM-07_25_50
Theory : list_1
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