Nuprl Lemma : imax-list-is-nat
∀L:ℤ List. (imax-list([0 / L]) ∈ ℕ)
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
cons: [a / b],
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
imax-list-cons-is-nat,
false_wf,
le_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesis,
intEquality
Latex:
\mforall{}L:\mBbbZ{} List. (imax-list([0 / L]) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-00_32_35
Last ObjectModification:
2018_05_19-AM-06_42_23
Theory : list_1
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