Nuprl Lemma : decide-spread-sq2
∀[x:Top × Top]. ∀[f,g,h:Top].
(case let a,b = x in inr f[a;b] of inl(z) => g[z] | inr(z) => h[z] ~ h[f[fst(x);snd(x)]])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
spread: spread def,
product: x:A × B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
inr: inr x ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache,
productEquality
Latex:
\mforall{}[x:Top \mtimes{} Top]. \mforall{}[f,g,h:Top].
(case let a,b = x in inr f[a;b] of inl(z) => g[z] | inr(z) => h[z] \msim{} h[f[fst(x);snd(x)]])
Date html generated:
2018_05_21-PM-00_01_16
Last ObjectModification:
2018_01_28-PM-02_24_25
Theory : union
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