Nuprl Lemma : agree_on_common_weakening
∀[T:Type]. ∀as,bs:T List.  agree_on_common(T;as;bs) supposing as = bs ∈ (T List)
Proof
Definitions occuring in Statement : 
agree_on_common: agree_on_common(T;as;bs)
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
prop: ℙ
, 
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]
, 
true: True
, 
guard: {T}
, 
or: P ∨ Q
, 
and: P ∧ Q
, 
cand: A c∧ B
Lemmas referenced : 
length_wf_nat, 
equal_wf, 
nat_wf, 
list_induction, 
agree_on_common_wf, 
list_wf, 
list_ind_nil_lemma, 
list_ind_cons_lemma, 
not_wf, 
l_member_wf, 
cons_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
lambdaFormation, 
cut, 
introduction, 
axiomEquality, 
hypothesis, 
thin, 
rename, 
dependent_set_memberEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
independent_functionElimination, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
natural_numberEquality, 
inrFormation, 
independent_pairFormation, 
productEquality, 
because_Cache, 
hyp_replacement, 
equalitySymmetry, 
applyLambdaEquality, 
setElimination, 
universeIsType, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}as,bs:T  List.    agree\_on\_common(T;as;bs)  supposing  as  =  bs
Date html generated:
2019_10_15-AM-10_53_02
Last ObjectModification:
2018_09_27-AM-11_04_15
Theory : list!
Home
Index