### Nuprl Lemma : singleton-type-void-domain

`∀[A:Type]. ∀[B:A ⟶ Type].  singleton-type(a:A ⟶ B[a]) supposing ¬A`

Proof

Definitions occuring in Statement :  singleton-type: `singleton-type(A)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` not: `¬A` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` not: `¬A` implies: `P `` Q` false: `False` singleton-type: `singleton-type(A)` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` so_apply: `x[s]` prop: `ℙ` so_lambda: `λ2x.t[x]`
Lemmas referenced :  it_wf all_wf equal_wf not_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction sqequalRule sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality voidElimination rename dependent_pairFormation lemma_by_obid hypothesis applyEquality independent_functionElimination cumulativity lambdaFormation functionExtensionality functionEquality isectElimination universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].    singleton-type(a:A  {}\mrightarrow{}  B[a])  supposing  \mneg{}A

Date html generated: 2016_05_14-PM-04_02_07
Last ObjectModification: 2015_12_26-PM-07_43_17

Theory : equipollence!!cardinality!

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