Nuprl Lemma : bag-null-rep
∀[n:ℕ]. ∀[x:Top]. (bag-null(bag-rep(n;x)) ~ (n =z 0))
Proof
Definitions occuring in Statement :
bag-rep: bag-rep(n;x),
bag-null: bag-null(bs),
nat: ℕ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
top: Top,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
bag-null_wf,
top_wf,
bag-rep_wf,
eq_int_wf,
subtype_base_sq,
bool_subtype_base,
null-bag-size,
list-subtype-bag,
bag-size-rep,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
sqequalRule,
setElimination,
rename,
natural_numberEquality,
instantiate,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:Top]. (bag-null(bag-rep(n;x)) \msim{} (n =\msubz{} 0))
Date html generated:
2016_05_15-PM-02_34_09
Last ObjectModification:
2015_12_27-AM-09_46_45
Theory : bags
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