Nuprl Lemma : lifting-bag-combine-decide
∀[a,F,G,f:Top].
(⋃b∈case a of inl(x) => F[x] | inr(x) => G[x].f[b] ~ case a 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],
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 :
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
uimplies: b supposing a
Lemmas referenced :
lifting-strict-decide,
top_wf,
strict4-bag-combine
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
thin,
baseClosed,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
cut,
lemma_by_obid,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
independent_isectElimination
Latex:
\mforall{}[a,F,G,f:Top].
(\mcup{}b\mmember{}case a of inl(x) => F[x] | inr(x) => G[x].f[b] \msim{} case a
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_09_47
Last ObjectModification:
2016_01_16-AM-08_33_50
Theory : bags
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