Nuprl Lemma : strong-subtype-union-base
∀[A:Type]. (strong-subtype(A;A ⋃ Base) ∧ strong-subtype(A;Base ⋃ A))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
strong-subtype: strong-subtype(A;B)
Lemmas referenced :
strong-subtype_witness,
b-union_wf,
base_wf,
strong-subtype-b-union-better,
strong-subtype-isect-base,
strong-subtype_transitivity,
strong-subtype-ext-equal,
subtype_rel_b-union_iff,
subtype_rel_b-union-right,
subtype_rel_b-union-left
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
because_Cache,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A:Type]. (strong-subtype(A;A \mcup{} Base) \mwedge{} strong-subtype(A;Base \mcup{} A))
Date html generated:
2016_05_13-PM-04_11_54
Last ObjectModification:
2015_12_26-AM-11_12_19
Theory : subtype_1
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