Nuprl Lemma : decide-trivial
∀[x:Top + Top]. ∀[y:Top]. (case x of inl(z) => y | inr(z) => y ~ y)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
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,
because_Cache,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
unionEquality
Latex:
\mforall{}[x:Top + Top]. \mforall{}[y:Top]. (case x of inl(z) => y | inr(z) => y \msim{} y)
Date html generated:
2016_05_15-PM-03_25_40
Last ObjectModification:
2015_12_27-PM-01_07_10
Theory : general
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