Nuprl Lemma : p-conditional-to-p-first
∀[A,B:Type]. ∀[f,g:A ⟶ (B + Top)]. ([f?g] = p-first([f; g]) ∈ (A ⟶ (B + Top)))
Proof
Definitions occuring in Statement :
p-conditional: [f?g],
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),
p-conditional: [f?g],
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
can-apply: can-apply(f;x),
implies: P ⇒ Q,
isl: isl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: ℙ
Lemmas referenced :
top_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
hypothesisEquality,
hypothesis,
functionEquality,
cumulativity,
unionEquality,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
because_Cache,
universeEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
applyEquality,
lambdaFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[f,g:A {}\mrightarrow{} (B + Top)]. ([f?g] = p-first([f; g]))
Date html generated:
2017_10_01-AM-09_14_10
Last ObjectModification:
2017_07_26-PM-04_49_21
Theory : general
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