Nuprl Lemma : pi1_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[p:a:A × B[a]]. (fst(p) ∈ A)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi1: fst(t),
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
applyEquality,
isect_memberEquality,
isectElimination,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[p:a:A \mtimes{} B[a]]. (fst(p) \mmember{} A)
Date html generated:
2016_05_13-PM-03_08_28
Last ObjectModification:
2016_01_06-PM-05_27_33
Theory : core_2
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