Nuprl Lemma : list-diff-diff
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs,cs:T List]. (as-bs-cs = as-bs @ cs ∈ (T List))
Proof
Definitions occuring in Statement :
list-diff: as-bs,
append: as @ bs,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
list-diff: as-bs,
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
all: ∀x:A. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
false: False,
guard: {T}
Lemmas referenced :
assert-deq-member,
assert_of_bnot,
assert_of_band,
iff_weakening_uiff,
iff_transitivity,
assert_wf,
not_wf,
and_wf,
iff_wf,
or_wf,
member_append,
append_wf,
deq-member_wf,
bnot_wf,
band_wf,
iff_imp_equal_bool,
deq_wf,
l_member_wf,
filter_wf5,
filter-filter
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
because_Cache,
hypothesisEquality,
setEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
setElimination,
rename,
independent_isectElimination,
addLevel,
productElimination,
independent_pairFormation,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination,
impliesLevelFunctionality,
lambdaFormation,
unionElimination,
inlFormation,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs,cs:T List]. (as-bs-cs = as-bs @ cs)
Date html generated:
2016_05_14-PM-03_29_57
Last ObjectModification:
2016_01_14-PM-11_21_06
Theory : decidable!equality
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