Nuprl Lemma : ocgrp_subtype_abdgrp
OGrp ⊆r AbDGrp
Proof
Definitions occuring in Statement :
ocgrp: OGrp,
abdgrp: AbDGrp,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
abdgrp: AbDGrp,
all: ∀x:A. B[x],
ocgrp: OGrp,
ocmon: OCMon,
omon: OMon,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
infix_ap: x f y,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
abgrp: AbGrp,
grp: Group{i}
Lemmas referenced :
ocgrp_subtype_abgrp,
omon_properties,
subtype_rel_sets,
abmonoid_wf,
ulinorder_wf,
grp_car_wf,
assert_wf,
infix_ap_wf,
bool_wf,
grp_le_wf,
equal_wf,
grp_eq_wf,
eqtt_to_assert,
cancel_wf,
grp_op_wf,
uall_wf,
monot_wf,
inverse_wf,
grp_id_wf,
grp_inv_wf,
set_wf,
eqfun_p_wf,
ocgrp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
dependent_set_memberEquality,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
dependent_functionElimination,
thin,
instantiate,
isectElimination,
setEquality,
productEquality,
setElimination,
rename,
because_Cache,
functionEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
cumulativity,
universeEquality,
independent_pairFormation,
addLevel,
levelHypothesis
Latex:
OGrp \msubseteq{}r AbDGrp
Date html generated:
2017_10_01-AM-08_15_12
Last ObjectModification:
2017_02_28-PM-02_00_21
Theory : groups_1
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