Nuprl Lemma : p-conditional_wf
∀[A,B:Type]. ∀[f,g:A ⟶ (B + Top)]. ([f?g] ∈ A ⟶ (B + Top))
Proof
Definitions occuring in Statement :
p-conditional: [f?g],
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-conditional: [f?g],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
ifthenelse_wf,
can-apply_wf,
subtype_rel_dep_function,
top_wf,
subtype_rel_union
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
unionEquality,
hypothesis,
because_Cache,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f,g:A {}\mrightarrow{} (B + Top)]. ([f?g] \mmember{} A {}\mrightarrow{} (B + Top))
Date html generated:
2016_05_15-PM-03_30_31
Last ObjectModification:
2015_12_27-PM-01_10_35
Theory : general
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