Nuprl Lemma : nim-grp_wf
nim-grp() ∈ AbDGrp
Proof
Definitions occuring in Statement :
nim-grp: nim-grp(),
member: t ∈ T,
abdgrp: AbDGrp
Definitions unfolded in proof :
member: t ∈ T,
abdgrp: AbDGrp,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
nim-grp: nim-grp(),
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
monoid_p: IsMonoid(T;op;id),
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
grp_id: e,
ident: Ident(T;op;id),
assoc: Assoc(T;op),
infix_ap: x f y,
all: ∀x:A. B[x],
top: Top,
cand: A c∧ B,
ge: i ≥ j ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
inverse: Inverse(T;op;id;inv),
grp_inv: ~,
comm: Comm(T;op),
eqfun_p: IsEqFun(T;eq),
grp_eq: =b,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
nat_wf,
eq_int_wf,
le_int_wf,
nim-sum_wf,
false_wf,
le_wf,
bool_wf,
nim_sum0_lemma,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
nim-sum-assoc,
nim-sum-0,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
nim-sum-same,
inverse_wf,
grp_inv_wf,
nim-sum-com,
comm_wf,
assert_of_eq_int,
assert_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
assert_witness,
equal_wf,
eqfun_p_wf,
grp_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
dependent_pairEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
lambdaEquality,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
functionEquality,
productEquality,
cumulativity,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
applyEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
axiomEquality,
productElimination,
independent_pairEquality
Latex:
nim-grp() \mmember{} AbDGrp
Date html generated:
2018_05_21-PM-09_15_43
Last ObjectModification:
2018_05_19-PM-05_15_05
Theory : general
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