Nuprl Lemma : strong-subtype-isect-base
∀[A:Type]. (strong-subtype(A ⋂ Base;Base) ∧ strong-subtype(Base ⋂ A;Base))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
isect2: T1 ⋂ T2,
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,
strong-subtype: strong-subtype(A;B),
subtype_rel: A ⊆r B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
exists: ∃x:A. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
isect2_subtype_rel2,
base_wf,
subtype_base_sq,
subtype_rel_self,
isect2_subtype_rel,
bool_wf,
exists_wf,
isect2_wf,
equal_wf,
strong-subtype_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
lambdaEquality,
isect_memberEquality,
unionElimination,
equalityElimination,
sqequalRule,
setElimination,
rename,
productElimination,
instantiate,
cumulativity,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
setEquality,
independent_pairEquality,
universeEquality
Latex:
\mforall{}[A:Type]. (strong-subtype(A \mcap{} Base;Base) \mwedge{} strong-subtype(Base \mcap{} A;Base))
Date html generated:
2016_05_13-PM-04_11_52
Last ObjectModification:
2015_12_26-AM-11_21_25
Theory : subtype_1
Home
Index