Nuprl Lemma : p-first-singleton
∀[A,B:Type]. ∀[f:A ⟶ (B + Top)]. (p-first([f]) = f ∈ (A ⟶ (B + Top)))
Proof
Definitions occuring in Statement :
p-first: p-first(L),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-first: p-first(L),
list_accum: list_accum,
cons: [a / b],
nil: [],
it: ⋅
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
functionEquality,
unionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} (B + Top)]. (p-first([f]) = f)
Date html generated:
2016_05_15-PM-03_30_18
Last ObjectModification:
2015_12_27-PM-01_10_24
Theory : general
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