Nuprl Lemma : test_sqtype1
∀[X,Y:Type].  (SQType((n:ℕ × {L:𝔹 List| True} ? × (X + Y)) List)) supposing ((Y ⊆r Base) and (X ⊆r Base))
Proof
Definitions occuring in Statement : 
list: T List
, 
nat: ℕ
, 
bool: 𝔹
, 
sq_type: SQType(T)
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
true: True
, 
unit: Unit
, 
set: {x:A| B[x]} 
, 
product: x:A × B[x]
, 
union: left + right
, 
base: Base
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
nat: ℕ
Lemmas referenced : 
subtype_rel_wf, 
base_wf, 
equal_wf, 
list_wf, 
nat_wf, 
bool_wf, 
true_wf, 
unit_wf2, 
le_wf, 
subtype_base_sq, 
list_subtype_base, 
product_subtype_base, 
union_subtype_base, 
set_subtype_base, 
int_subtype_base, 
bool_subtype_base, 
unit_subtype_base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
lambdaEquality, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
sqequalAxiom, 
hypothesis, 
because_Cache, 
extract_by_obid, 
isectElimination, 
cumulativity, 
isect_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
productEquality, 
unionEquality, 
setEquality, 
intEquality, 
natural_numberEquality, 
instantiate, 
independent_isectElimination, 
lambdaFormation
Latex:
\mforall{}[X,Y:Type].
    (SQType((n:\mBbbN{}  \mtimes{}  \{L:\mBbbB{}  List|  True\}  ?  \mtimes{}  (X  +  Y))  List))  supposing  ((Y  \msubseteq{}r  Base)  and  (X  \msubseteq{}r  Base))
Date html generated:
2017_04_14-AM-09_27_38
Last ObjectModification:
2017_02_27-PM-04_01_07
Theory : list_1
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