Nuprl Lemma : super-fact_wf
∀[n:ℕ]. ((n)!! ∈ ℕ+)
Proof
Definitions occuring in Statement : 
super-fact: (n)!!
, 
nat_plus: ℕ+
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
super-fact: (n)!!
, 
nat_plus: ℕ+
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
true: True
, 
and: P ∧ Q
, 
prop: ℙ
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
guard: {T}
, 
ge: i ≥ j 
, 
lelt: i ≤ j < k
, 
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
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
Lemmas referenced : 
nat_wf, 
int_seg_wf, 
le_wf, 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
itermAdd_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
nat_properties, 
int_seg_properties, 
nat_plus_properties, 
fact_wf, 
mul_nat_plus, 
less_than_wf, 
nat_plus_wf, 
primrec_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
hypothesisEquality, 
dependent_set_memberEquality, 
natural_numberEquality, 
independent_pairFormation, 
imageMemberEquality, 
baseClosed, 
lambdaEquality, 
addEquality, 
setElimination, 
rename, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
computeAll, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}].  ((n)!!  \mmember{}  \mBbbN{}\msupplus{})
Date html generated:
2018_05_21-PM-01_04_33
Last ObjectModification:
2018_01_28-PM-02_13_11
Theory : num_thy_1
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