Nuprl Lemma : test-arith-length-additions
∀T:Type. ∀a:T. ∀b:T List. ∀i:ℤ. (i < ||[a / b]|| ⇒ i < ||b|| + 1)
Proof
Definitions occuring in Statement :
length: ||as||,
cons: [a / b],
list: T List,
less_than: a < b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
top: Top
Lemmas referenced :
less_than_wf,
length_wf,
cons_wf,
list_wf,
length_of_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
intEquality,
universeEquality,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}T:Type. \mforall{}a:T. \mforall{}b:T List. \mforall{}i:\mBbbZ{}. (i < ||[a / b]|| {}\mRightarrow{} i < ||b|| + 1)
Date html generated:
2016_05_14-AM-06_33_56
Last ObjectModification:
2015_12_26-PM-00_36_04
Theory : list_0
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