Nuprl Lemma : zhgrp_to_nat_is_hom
IsMonHom{<ℤ+>↓hgrp,<ℕ,+>}(λn.nat(n))
Proof
Definitions occuring in Statement :
int_hgrp_to_nat: nat(n),
nat_add_mon: <ℕ,+>,
int_add_grp: <ℤ+>,
hgrp_of_ocgrp: g↓hgrp,
monoid_hom_p: IsMonHom{M1,M2}(f),
lambda: λx.A[x]
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
and: P ∧ Q,
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),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
grp_id: e,
int_hgrp_to_nat: nat(n),
hgrp_of_ocgrp: g↓hgrp,
int_add_grp: <ℤ+>,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
le_wf,
false_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
int_hgrp_to_nat_wf,
add_nat_wf,
int_add_grp_wf2,
hgrp_of_ocgrp_wf,
grp_car_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
hypothesisEquality,
axiomEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation
Latex:
IsMonHom\{<\mBbbZ{}+>\mdownarrow{}hgrp,<\mBbbN{},+>\}(\mlambda{}n.nat(n))
Date html generated:
2016_05_15-PM-00_19_39
Last ObjectModification:
2016_01_15-PM-11_05_45
Theory : groups_1
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