Nuprl Lemma : not-canonicalizable-implies-subtype-base
¬(∀[T:Type]. (canonicalizable(T) ⇒ (T ⊆r Base)))
Proof
Definitions occuring in Statement :
canonicalizable: canonicalizable(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
guard: {T},
sq_type: SQType(T),
has-value: (a)↓,
true: True,
is-exception: is-exception(t)
Lemmas referenced :
uall_wf,
canonicalizable_wf,
subtype_rel_wf,
base_wf,
nat_wf,
canonicalizable-nat-to-nat,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__le,
intformand_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
le_wf,
equal_functionality_wrt_subtype_rel2,
and_wf,
equal_wf,
subtype_base_sq,
subtype_rel_self,
has-value_wf_base,
is-exception_wf,
bottom-sqle,
exception-not-value_1,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
functionEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
functionExtensionality,
setElimination,
rename,
dependent_functionElimination,
addEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
because_Cache,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
productElimination,
baseApply,
closedConclusion,
baseClosed,
sqequalSqle,
divergentSqle,
callbyvalueAdd,
isintReduceTrue,
addExceptionCases,
axiomSqleEquality,
sqleReflexivity
Latex:
\mneg{}(\mforall{}[T:Type]. (canonicalizable(T) {}\mRightarrow{} (T \msubseteq{}r Base)))
Date html generated:
2017_04_17-AM-10_02_15
Last ObjectModification:
2017_02_27-PM-05_53_45
Theory : continuity
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