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:
2016_05_15-PM-03_25_04
Last ObjectModification:
2015_12_27-PM-01_06_32
Theory : general
Home
Index