Nuprl Lemma : int_add_grp_wf
<ℤ+> ∈ AbGrp
Proof
Definitions occuring in Statement :
int_add_grp: <ℤ+>,
abgrp: AbGrp,
member: t ∈ T
Definitions unfolded in proof :
int_add_grp: <ℤ+>,
member: t ∈ T,
abgrp: AbGrp,
uall: ∀[x:A]. B[x],
grp: Group{i},
mon: Mon,
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),
and: P ∧ Q,
cand: A c∧ B,
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t)
Lemmas referenced :
int_term_value_minus_lemma,
itermMinus_wf,
int_term_value_constant_lemma,
itermConstant_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
le_int_wf,
eq_int_wf,
mk_grp,
grp_op_wf,
grp_car_wf,
comm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
intEquality,
lambdaEquality,
addEquality,
natural_numberEquality,
minusEquality,
independent_isectElimination,
sqequalRule,
isect_memberFormation,
introduction,
dependent_functionElimination,
because_Cache,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
independent_pairFormation,
productElimination,
independent_pairEquality
Latex:
<\mBbbZ{}+> \mmember{} AbGrp
Date html generated:
2016_05_15-PM-00_17_37
Last ObjectModification:
2016_01_15-PM-11_04_34
Theory : groups_1
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