Nuprl Lemma : nat_int_grp_sig_hom
IsMonHomInj(<ℕ,+>;<ℤ+>;λx.x)
Proof
Definitions occuring in Statement :
nat_add_mon: <ℕ,+>,
int_add_grp: <ℤ+>,
mon_hom_inj_p: IsMonHomInj(g;h;f),
lambda: λx.A[x]
Definitions unfolded in proof :
mon_hom_inj_p: IsMonHomInj(g;h;f),
and: P ∧ Q,
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_add_mon: <ℕ,+>,
grp_car: |g|,
pi1: fst(t),
int_add_grp: <ℤ+>,
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
nat: ℕ,
grp_id: e,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
equal_wf,
le_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
itermConstant_wf,
intformle_wf,
decidable__le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
addEquality,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
lemma_by_obid,
isect_memberEquality,
isectElimination,
axiomEquality,
because_Cache,
natural_numberEquality,
lambdaFormation,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality
Latex:
IsMonHomInj(<\mBbbN{},+><\mBbbZ{}+>\mlambda{}x.x)
Date html generated:
2016_05_15-PM-00_17_54
Last ObjectModification:
2016_01_15-PM-11_06_01
Theory : groups_1
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