Nuprl Lemma : subtype_bar2
∀[A,B:Type]. bar(A) ⊆r bar(B) supposing (A ⊆r B) ∧ (value-type(A) ∨ (A ⊆r Base)) ∧ (value-type(B) ∨ (B ⊆r Base))
Proof
Definitions occuring in Statement :
bar: bar(T),
value-type: value-type(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
and: P ∧ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
bar: bar(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
base_wf,
value-type_wf,
or_wf,
subtype_rel_wf,
and_wf,
subtype_rel_partial
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type].
bar(A) \msubseteq{}r bar(B)
supposing (A \msubseteq{}r B) \mwedge{} (value-type(A) \mvee{} (A \msubseteq{}r Base)) \mwedge{} (value-type(B) \mvee{} (B \msubseteq{}r Base))
Date html generated:
2016_05_15-PM-10_03_46
Last ObjectModification:
2016_01_05-PM-06_26_46
Theory : bar!type
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