Nuprl Lemma : posint_mul_mon_wf
<ℤ+,*> ∈ AbMon
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
member: t ∈ T,
abmonoid: AbMon
Definitions unfolded in proof :
posint_mul_mon: <ℤ+,*>,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
ident: Ident(T;op;id),
cand: A c∧ B,
guard: {T},
comm: Comm(T;op)
Lemmas referenced :
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformless_wf,
intformand_wf,
decidable__lt,
int_term_value_constant_lemma,
itermConstant_wf,
mul_bounds_1b,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermMultiply_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_plus_properties,
less_than_wf,
mul_nat_plus,
le_int_wf,
eq_int_wf,
nat_plus_wf,
mk_abmonoid
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
introduction,
imageMemberEquality,
baseClosed,
independent_isectElimination,
isect_memberFormation,
dependent_functionElimination,
multiplyEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
setEquality,
productElimination,
independent_pairEquality
Latex:
<\mBbbZ{}\msupplus{},*> \mmember{} AbMon
Date html generated:
2016_05_16-AM-07_45_31
Last ObjectModification:
2016_01_16-PM-11_37_55
Theory : factor_1
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