Nuprl Lemma : cons-bag-as-append
∀[x,b:Top]. (x.b ~ {x} + b)
Proof
Definitions occuring in Statement :
bag-append: as + bs,
cons-bag: x.b,
single-bag: {x},
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
single-bag: {x},
bag-append: as + bs,
cons-bag: x.b,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_ind_cons_lemma,
list_ind_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[x,b:Top]. (x.b \msim{} \{x\} + b)
Date html generated:
2016_05_15-PM-02_22_36
Last ObjectModification:
2015_12_27-AM-09_54_38
Theory : bags
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