### 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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