Nuprl Lemma : pos_length3
∀[A:Type]. ∀[l:A List]. uiff(¬↑null(l);||l|| ≥ 1 )
Proof
Definitions occuring in Statement :
length: ||as||,
null: null(as),
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
not: ¬A,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B
Lemmas referenced :
list_wf,
ge_wf,
decidable__lt,
null_wf,
assert_wf,
not_wf,
less_than'_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
length_wf,
decidable__le,
pos_length2
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_pairFormation,
productElimination,
introduction,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List]. uiff(\mneg{}\muparrow{}null(l);||l|| \mgeq{} 1 )
Date html generated:
2016_05_14-AM-07_39_04
Last ObjectModification:
2016_01_15-AM-08_37_05
Theory : list_1
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