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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