Nuprl Lemma : list-diff-disjoint
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:T List]. as-bs = as ∈ (T List) supposing l_disjoint(T;as;bs)
Proof
Definitions occuring in Statement :
list-diff: as-bs,
l_disjoint: l_disjoint(T;l1;l2),
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
list-diff: as-bs,
all: ∀x:A. B[x],
top: Top,
l_disjoint: l_disjoint(T;l1;l2),
not: ¬A,
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
false: False,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
l_disjoint_wf,
equal_wf,
list-diff_wf,
filter_nil_lemma,
nil_wf,
cons_wf,
deq_wf,
cons_member,
l_member_wf,
squash_wf,
true_wf,
list-diff-cons,
iff_weakening_equal,
deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaFormation,
rename,
independent_isectElimination,
universeEquality,
productElimination,
inrFormation,
independent_pairFormation,
productEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
unionElimination,
equalityElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
inlFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:T List]. as-bs = as supposing l\_disjoint(T;as;bs)
Date html generated:
2017_04_17-AM-09_13_17
Last ObjectModification:
2017_02_27-PM-05_20_31
Theory : decidable!equality
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