Nuprl Lemma : super-fact-unroll
∀[n:ℕ+]. ((n)!! ~ (n)! * (n - 1)!!)
Proof
Definitions occuring in Statement :
super-fact: (n)!!,
fact: (n)!,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
multiply: n * m,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
super-fact: (n)!!,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
nat: ℕ
Lemmas referenced :
mul_bounds_1b,
int_term_value_mul_lemma,
itermMultiply_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
le_wf,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
intformle_wf,
intformnot_wf,
decidable__le,
subtract-add-cancel,
neg_assert_of_eq_int,
assert-bnot,
bool_subtype_base,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
less_than_wf,
nat_plus_wf,
super-fact_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
fact_wf,
decidable__equal_int,
nat_plus_properties,
assert_of_eq_int,
eqtt_to_assert,
bool_wf,
eq_int_wf,
primrec-unroll,
int_subtype_base,
set_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
sqequalRule,
hypothesis,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
multiplyEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
applyEquality,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
promote_hyp,
cumulativity,
independent_functionElimination,
addEquality,
equalityEquality,
sqequalAxiom
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. ((n)!! \msim{} (n)! * (n - 1)!!)
Date html generated:
2016_05_15-PM-04_08_38
Last ObjectModification:
2016_01_16-AM-11_03_07
Theory : general
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