Nuprl Lemma : agree_on_common_cons
∀[T:Type]. ∀as,bs:T List. ∀x:T. (agree_on_common(T;[x / as];[x / bs]) ⇐⇒ agree_on_common(T;as;bs))
Proof
Definitions occuring in Statement :
agree_on_common: agree_on_common(T;as;bs),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_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],
or: P ∨ Q,
not: ¬A,
false: False,
guard: {T},
cand: A c∧ B
Lemmas referenced :
agree_on_common_wf,
cons_wf,
list_wf,
list_ind_cons_lemma,
cons_member,
l_member_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
universeEquality,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
productElimination,
independent_functionElimination,
inlFormation,
inrFormation,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. \mforall{}x:T. (agree\_on\_common(T;[x / as];[x / bs]) \mLeftarrow{}{}\mRightarrow{} agree\_on\_common(T;as;bs))
Date html generated:
2019_10_15-AM-10_53_00
Last ObjectModification:
2018_09_27-AM-11_02_33
Theory : list!
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