Nuprl Lemma : alttree_wf
∀[T:Type]. ∀[X:n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹]. (Tree(X) ∈ ℙ)
Proof
Definitions occuring in Statement :
alttree: Tree(A),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
guard: {T},
sq_stable: SqStable(P),
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
alttree: Tree(A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
bool_wf,
istype-nat,
subtype_rel_self,
le_weakening2,
sq_stable__le,
istype-false,
int_seg_subtype,
subtype_rel_function,
istype-le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
assert_wf,
int_seg_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
Error :functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
baseClosed,
imageMemberEquality,
Error :lambdaFormation_alt,
Error :universeIsType,
independent_pairFormation,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
Error :lambdaEquality_alt,
Error :dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
imageElimination,
productElimination,
Error :dependent_set_memberEquality_alt,
because_Cache,
applyEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[X:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} \mBbbB{}]. (Tree(X) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_46_09
Last ObjectModification:
2019_06_06-PM-01_27_38
Theory : fan-theorem
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