Nuprl Lemma : agree_on_common_iseg
∀[T:Type]
∀as2,bs2,as1,bs1:T List. (as1 ≤ as2 ⇒ bs1 ≤ bs2 ⇒ agree_on_common(T;as2;bs2) ⇒ agree_on_common(T;as1;bs1))
Proof
Definitions occuring in Statement :
agree_on_common: agree_on_common(T;as;bs),
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
agree_on_common: agree_on_common(T;as;bs),
list_ind: list_ind,
nil: [],
it: ⋅,
true: True,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
rev_implies: P ⇐ Q,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
or: P ∨ Q,
not: ¬A,
guard: {T},
false: False,
cand: A c∧ B
Lemmas referenced :
list_induction,
all_wf,
list_wf,
iseg_wf,
agree_on_common_wf,
istype-universe,
nil_wf,
iseg_nil,
assert_of_null,
cons_wf,
agree_on_common_nil,
list_ind_nil_lemma,
istype-void,
list_ind_cons_lemma,
cons_iseg,
not_wf,
l_member_wf,
cons_member,
iseg_member
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,
hypothesis,
because_Cache,
functionEquality,
inhabitedIsType,
universeIsType,
independent_functionElimination,
rename,
functionIsType,
dependent_functionElimination,
universeEquality,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
productElimination,
independent_isectElimination,
natural_numberEquality,
isect_memberEquality_alt,
voidElimination,
productIsType,
equalityIsType1,
unionElimination,
inlFormation_alt,
unionIsType,
inrFormation_alt,
independent_pairFormation,
promote_hyp,
equalityTransitivity
Latex:
\mforall{}[T:Type]
\mforall{}as2,bs2,as1,bs1:T List.
(as1 \mleq{} as2 {}\mRightarrow{} bs1 \mleq{} bs2 {}\mRightarrow{} agree\_on\_common(T;as2;bs2) {}\mRightarrow{} agree\_on\_common(T;as1;bs1))
Date html generated:
2019_10_15-AM-10_53_47
Last ObjectModification:
2018_10_09-AM-10_28_16
Theory : list!
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