Nuprl Lemma : decide-decide
∀[x:Top + Top]. ∀[f1,f2,g,h:Top].
(case case x of inl(z) => f1[z] | inr(z) => f2[z] of inl(z) => g[z] | inr(z) => h[z] ~ case x
of inl(z) =>
case f1[z] of inl(z) => g[z] | inr(z) => h[z]
| inr(z) =>
case f2[z] of inl(z) => g[z] | inr(z) => h[z])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
sqequalRule,
sqequalAxiom,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache,
unionEquality
Latex:
\mforall{}[x:Top + Top]. \mforall{}[f1,f2,g,h:Top].
(case case x of inl(z) => f1[z] | inr(z) => f2[z] of inl(z) => g[z] | inr(z) => h[z] \msim{} case x
of inl(z) =>
case f1[z] of inl(z) => g[z] | inr(z) => h[z]
| inr(z) =>
case f2[z] of inl(z) => g[z] | inr(z) => h[z])
Date html generated:
2018_05_21-PM-00_01_22
Last ObjectModification:
2018_01_28-PM-02_24_25
Theory : union
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