Nuprl Lemma : record-select_wf
∀[T:Atom ⟶ 𝕌']. ∀[z:Atom]. ∀[r:record(x.T[x])]. (r.z ∈ T[z])
Proof
Definitions occuring in Statement :
record-select: r.x,
record: record(x.T[x]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
record: record(x.T[x]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
record-select: r.x,
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
atomEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Atom {}\mrightarrow{} \mBbbU{}']. \mforall{}[z:Atom]. \mforall{}[r:record(x.T[x])]. (r.z \mmember{} T[z])
Date html generated:
2016_05_15-PM-06_40_15
Last ObjectModification:
2015_12_27-AM-11_52_52
Theory : general
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