Nuprl Lemma : urec_subtype_base
∀[F:Type ⟶ Type]. urec(F) ⊆r Base supposing ∀T:Type. ((T ⊆r Base) ⇒ ((F T) ⊆r Base))
Proof
Definitions occuring in Statement :
urec: urec(F),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
urec: urec(F),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
guard: {T}
Lemmas referenced :
subtype_rel_wf,
all_wf,
base_wf,
subtype_rel_transitivity,
subtype_rel_self,
subtract-add-cancel,
fun_exp_add1,
le_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
fun_exp0_lemma,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
fun_exp_wf,
nat_wf,
tunion_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
instantiate,
universeEquality,
hypothesisEquality,
voidEquality,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
unionElimination,
dependent_set_memberEquality,
because_Cache,
addEquality,
cumulativity,
functionEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. urec(F) \msubseteq{}r Base supposing \mforall{}T:Type. ((T \msubseteq{}r Base) {}\mRightarrow{} ((F T) \msubseteq{}r Base))
Date html generated:
2016_05_15-PM-06_51_05
Last ObjectModification:
2016_01_16-AM-09_51_28
Theory : general
Home
Index