Nuprl Lemma : rng_mssum_elim_lemma
∀[s,r,as,f:Top]. (Σx ∈ mk_mset(as). f[x] ~ Σ{r} x ∈ as. f[x])
Proof
Definitions occuring in Statement :
rng_mssum: rng_mssum,
mk_mset: mk_mset(as),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t,
rng_lsum: Σ{r} x ∈ as. f[x]
Definitions unfolded in proof :
rng_lsum: Σ{r} x ∈ as. f[x],
mk_mset: mk_mset(as),
rng_mssum: rng_mssum,
mset_for: mset_for,
mon_for: For{g} x ∈ as. f[x],
add_grp_of_rng: r↓+gp,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
grp_id: e,
for: For{T,op,id} x ∈ as. f[x],
tlambda: λx:T. b[x],
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[s,r,as,f:Top]. (\mSigma{}x \mmember{} mk\_mset(as). f[x] \msim{} \mSigma{}\{r\} x \mmember{} as. f[x])
Date html generated:
2018_05_22-AM-07_46_04
Last ObjectModification:
2018_05_19-AM-08_30_25
Theory : list_3
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