Nuprl Lemma : lifting-bag-combine-decide-name_eq
∀[a,b,F,G,f:Top].
(⋃b∈case name_eq(a;b) of inl(x) => F[x] | inr(x) => G[x].f[b] ~ case name_eq(a;b)
of inl(x) =>
⋃b∈F[x].f[b]
| inr(x) =>
⋃b∈G[x].f[b])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
name_eq: name_eq(x;y),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
lifting-bag-combine-decide,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[a,b,F,G,f:Top].
(\mcup{}b\mmember{}case name\_eq(a;b) of inl(x) => F[x] | inr(x) => G[x].f[b] \msim{} case name\_eq(a;b)
of inl(x) =>
\mcup{}b\mmember{}F[x].f[b]
| inr(x) =>
\mcup{}b\mmember{}G[x].f[b])
Date html generated:
2016_05_15-PM-03_10_20
Last ObjectModification:
2015_12_27-AM-09_25_11
Theory : bags
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