Nuprl Lemma : rec-value_subype_base
rec-value() ⊆r Base
Proof
Definitions occuring in Statement :
rec-value: rec-value(),
subtype_rel: A ⊆r B,
base: Base
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
ext-eq: A ≡ B,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
atomic-values: atomic-values(),
Value: Value(),
pi2: snd(t),
rec-value-height: rec-value-height(v),
co-value-height: co-value-height(t),
le: A ≤ B,
outl: outl(x),
uiff: uiff(P;Q),
outr: outr(x)
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
int_seg_properties,
int_seg_wf,
subtract-1-ge-0,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le,
decidable__lt,
istype-le,
subtype_rel_self,
istype-nat,
rec-value-ext,
subtract_nat_wf,
rec-value-height_wf,
itermAdd_wf,
int_term_value_add_lemma,
add-is-int-iff,
false_wf,
rec-value_wf,
nat_wf,
satisfiable-full-omega-tt
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
productElimination,
because_Cache,
unionElimination,
applyEquality,
instantiate,
applyLambdaEquality,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
hypothesis_subsumption,
promote_hyp,
imageElimination,
equalityElimination,
Error :equalityIsType1,
baseApply,
closedConclusion,
baseClosed,
pointwiseFunctionality,
addEquality,
computeAll,
voidEquality,
isect_memberEquality,
intEquality,
dependent_pairFormation,
lemma_by_obid,
lambdaEquality
Latex:
rec-value() \msubseteq{}r Base
Date html generated:
2019_06_20-PM-01_54_31
Last ObjectModification:
2018_10_17-PM-01_20_26
Theory : rec_values
Home
Index