Nuprl Lemma : fact-non-zero
∀[m:ℕ]. (¬((m)! = 0 ∈ ℤ))
Proof
Definitions occuring in Statement :
fact: (n)!,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat_plus: ℕ+
Lemmas referenced :
fact-positive,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
equal-wf-T-base,
fact_wf,
nat_plus_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
applyEquality,
because_Cache,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[m:\mBbbN{}]. (\mneg{}((m)! = 0))
Date html generated:
2018_05_21-PM-01_01_39
Last ObjectModification:
2018_01_28-PM-02_12_19
Theory : num_thy_1
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