Nuprl Lemma : bottom_wf_function
∀[A:Type]. ∀[B:A ⟶ Type]. ⊥ ∈ a:A ⟶ partial(B[a]) supposing ∀a:A. value-type(B[a])
Proof
Definitions occuring in Statement :
partial: partial(T),
bottom: ⊥,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
value-type_wf,
all_wf,
bottom_wf-partial,
strictness-apply
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mbot{} \mmember{} a:A {}\mrightarrow{} partial(B[a]) supposing \mforall{}a:A. value-type(B[a])
Date html generated:
2016_05_14-AM-06_09_47
Last ObjectModification:
2016_01_06-PM-08_35_12
Theory : partial_1
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