Nuprl Lemma : bag-append-ident
∀[T:Type]. ∀[as:bag(T)]. (((as + {}) = as ∈ bag(T)) ∧ (({} + as) = as ∈ bag(T)))
Proof
Definitions occuring in Statement :
bag-append: as + bs,
empty-bag: {},
bag: bag(T),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
bag-append-empty,
bag-subtype-list,
equal_wf,
squash_wf,
true_wf,
bag_wf,
bag-append-comm,
empty-bag_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
hypothesis,
independent_pairFormation,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
cumulativity,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as:bag(T)]. (((as + \{\}) = as) \mwedge{} ((\{\} + as) = as))
Date html generated:
2017_10_01-AM-08_45_04
Last ObjectModification:
2017_07_26-PM-04_30_32
Theory : bags
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