Nuprl Lemma : int-prod_wf_nat_plus
∀[n:ℕ]. ∀[f:ℕn ⟶ ℕ+]. (Π(f[x] | x < n) ∈ ℕ+)
Proof
Definitions occuring in Statement :
int-prod: Π(f[x] | x < k),
int_seg: {i..j-},
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
so_apply: x[s],
false: False,
prop: ℙ,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
nat: ℕ,
nat_plus: ℕ+,
int-prod: Π(f[x] | x < k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
int_seg_wf,
mul_nat_plus,
istype-less_than,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
istype-void,
int_formula_prop_not_lemma,
istype-int,
itermConstant_wf,
intformless_wf,
intformnot_wf,
full-omega-unsat,
decidable__lt,
nat_properties,
nat_plus_wf,
primrec_wf
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
universeIsType,
voidElimination,
isect_memberEquality_alt,
lambdaEquality_alt,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
rename,
setElimination,
natural_numberEquality,
dependent_set_memberEquality_alt,
hypothesisEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}\msupplus{}]. (\mPi{}(f[x] | x < n) \mmember{} \mBbbN{}\msupplus{})
Date html generated:
2019_10_15-AM-10_21_21
Last ObjectModification:
2019_10_10-PM-06_27_56
Theory : int_2
Home
Index