Nuprl Lemma : spread-spread
∀[t:Top × Top]. ∀[P,Q:Top]. (let x,y = let a,b = t in P[a;b] in Q[x;y] ~ let a,b = t in let x,y = P[a;b] in Q[x;y])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
product: x:A × B[x],
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,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
hypothesis,
because_Cache,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
lemma_by_obid,
productEquality
Latex:
\mforall{}[t:Top \mtimes{} Top]. \mforall{}[P,Q:Top].
(let x,y = let a,b = t
in P[a;b]
in Q[x;y] \msim{} let a,b = t
in let x,y = P[a;b]
in Q[x;y])
Date html generated:
2018_05_21-PM-00_01_26
Last ObjectModification:
2018_01_28-PM-02_24_27
Theory : union
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