Nuprl Lemma : pair_eta_rw
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[p:a:A × B[a]]. (<fst(p), snd(p)> = p ∈ (a:A × B[a]))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
pi1: fst(t),
pi2: snd(t)
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis,
Error :productIsType,
Error :universeIsType,
hypothesisEquality,
applyEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
productEquality,
Error :functionIsType,
Error :inhabitedIsType,
because_Cache,
functionEquality,
cumulativity,
universeEquality,
productElimination,
dependent_pairEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[p:a:A \mtimes{} B[a]]. (<fst(p), snd(p)> = p)
Date html generated:
2019_06_20-AM-11_14_42
Last ObjectModification:
2018_09_26-AM-10_42_03
Theory : core_2
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