Nuprl Lemma : fact_unroll_1
∀[n:ℤ]. (n)! ~ n * (n - 1)! supposing ¬n < 1
Proof
Definitions occuring in Statement :
fact: (n)!,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
multiply: n * m,
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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 ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
fact_unroll,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
independent_functionElimination,
voidElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
sqequalAxiom,
isect_memberEquality,
intEquality
Latex:
\mforall{}[n:\mBbbZ{}]. (n)! \msim{} n * (n - 1)! supposing \mneg{}n < 1
Date html generated:
2018_05_21-PM-01_00_47
Last ObjectModification:
2018_05_19-AM-06_37_34
Theory : num_thy_1
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