Nuprl Lemma : length_cons
∀[A:Type]. ∀[a:A]. ∀[as:A List]. (||[a / as]|| = (||as|| + 1) ∈ ℤ)
Proof
Definitions occuring in Statement :
length: ||as||,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
add: 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,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
length_of_cons_lemma,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
addEquality,
isectElimination,
hypothesisEquality,
natural_numberEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[a:A]. \mforall{}[as:A List]. (||[a / as]|| = (||as|| + 1))
Date html generated:
2016_05_14-AM-06_33_37
Last ObjectModification:
2015_12_26-PM-00_36_39
Theory : list_0
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