Nuprl Lemma : partition-mesh-nil
∀[I:Top]. (partition-mesh(I;[]) ~ |I|)
Proof
Definitions occuring in Statement :
partition-mesh: partition-mesh(I;p),
i-length: |I|,
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
partition-mesh: partition-mesh(I;p),
full-partition: full-partition(I;p),
frs-mesh: frs-mesh(p),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
lt_int: i <z j,
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
rmaximum: rmaximum(n;m;k.x[k]),
select: L[n],
cons: [a / b],
i-length: |I|
Lemmas referenced :
length_of_cons_lemma,
list_ind_nil_lemma,
length_of_nil_lemma,
primrec0_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}[I:Top]. (partition-mesh(I;[]) \msim{} |I|)
Date html generated:
2016_05_18-AM-08_56_39
Last ObjectModification:
2015_12_27-PM-11_37_32
Theory : reals
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