Nuprl Lemma : name_eq-normalize-left
∀[F,G,a,b:Top]. (case name_eq(a;b) of inl(x) => F a | inr(y) => G ~ case name_eq(a;b) of inl(x) => F b | inr(y) => G)
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
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,
ifthenelse: if b then t else f fi
Lemmas referenced :
name_eq-normalize,
top_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
sqequalRule,
isect_memberEquality
Latex:
\mforall{}[F,G,a,b:Top].
(case name\_eq(a;b) of inl(x) => F a | inr(y) => G \msim{} case name\_eq(a;b)
of inl(x) =>
F b
| inr(y) =>
G)
Date html generated:
2016_05_14-PM-03_34_59
Last ObjectModification:
2015_12_26-PM-05_59_41
Theory : decidable!equality
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