Nuprl Lemma : length_cons_ge_one
∀[x:Top]. ∀[l:Top List]. (||[x / l]|| ≥ 1 )
Proof
Definitions occuring in Statement :
length: ||as||,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
ge: i ≥ j ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
pos_length,
top_wf,
cons_wf,
cons_neq_nil,
less_than'_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[x:Top]. \mforall{}[l:Top List]. (||[x / l]|| \mgeq{} 1 )
Date html generated:
2016_05_14-AM-06_35_02
Last ObjectModification:
2015_12_26-PM-00_35_13
Theory : list_0
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