Nuprl Lemma : agree_on_common_nil
∀[T:Type]. ∀as:T List. (agree_on_common(T;as;[]) ⇐⇒ True)
Proof
Definitions occuring in Statement :
agree_on_common: agree_on_common(T;as;bs),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
agree_on_common: agree_on_common(T;as;bs),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
iff_wf,
agree_on_common_wf,
nil_wf,
true_wf,
list_ind_nil_lemma,
istype-void,
list_ind_cons_lemma,
istype-universe,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
because_Cache,
hypothesis,
universeIsType,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
natural_numberEquality,
rename,
productElimination,
productIsType,
functionIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}as:T List. (agree\_on\_common(T;as;[]) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2019_10_15-AM-10_53_05
Last ObjectModification:
2018_10_09-AM-10_31_08
Theory : list!
Home
Index