Nuprl Lemma : fact-positive
∀[m:ℕ]. (1 ≤ (m)!)
Proof
Definitions occuring in Statement :
fact: (n)!,
nat: ℕ,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
guard: {T},
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,
and: P ∧ Q,
le: A ≤ B
Lemmas referenced :
nat_wf,
less_than'_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
less_than_wf,
nat_plus_properties,
le_wf,
fact_wf,
decidable__le,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
dependent_set_memberEquality,
applyEquality,
because_Cache,
sqequalRule,
unionElimination,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
setEquality,
intEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[m:\mBbbN{}]. (1 \mleq{} (m)!)
Date html generated:
2016_05_15-PM-04_05_31
Last ObjectModification:
2016_01_16-AM-11_01_53
Theory : general
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