Nuprl Lemma : p-first_wf
∀[A,B:Type]. ∀[L:(A ⟶ (B + Top)) List]. (p-first(L) ∈ A ⟶ (B + Top))
Proof
Definitions occuring in Statement :
p-first: p-first(L),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
p-first: p-first(L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
top_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
unionEquality,
hypothesis,
inrEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
unionElimination,
inlEquality,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:(A {}\mrightarrow{} (B + Top)) List]. (p-first(L) \mmember{} A {}\mrightarrow{} (B + Top))
Date html generated:
2019_10_15-AM-11_07_25
Last ObjectModification:
2018_08_21-PM-01_58_59
Theory : general
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