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!
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