### Nuprl Lemma : assert_witness

[b:𝔹]. ((↑b)  (Ax ∈ ↑b))

Proof

Definitions occuring in Statement :  assert: b bool: 𝔹 uall: [x:A]. B[x] implies:  Q member: t ∈ T axiom: Ax
Definitions unfolded in proof :  assert: b uall: [x:A]. B[x] member: t ∈ T implies:  Q all: x:A. B[x] exposed-it: exposed-it bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a ifthenelse: if then else fi  true: True bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb false: False
Lemmas referenced :  bool_wf eqtt_to_assert eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base ifthenelse_wf true_wf false_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaFormation hypothesisEquality thin extract_by_obid hypothesis sqequalHypSubstitution unionElimination equalityElimination isectElimination because_Cache productElimination independent_isectElimination axiomEquality natural_numberEquality dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity equalityTransitivity equalitySymmetry independent_functionElimination voidElimination universeEquality lambdaEquality

Latex:
\mforall{}[b:\mBbbB{}].  ((\muparrow{}b)  {}\mRightarrow{}  (Ax  \mmember{}  \muparrow{}b))

Date html generated: 2019_06_20-AM-11_30_56
Last ObjectModification: 2018_08_01-AM-10_18_53

Theory : bool_1

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