Nuprl Lemma : grp_properties
∀[g:Group{i}]. Inverse(|g|;*;e;~)
Proof
Definitions occuring in Statement :
grp: Group{i},
grp_inv: ~,
grp_id: e,
grp_op: *,
grp_car: |g|,
inverse: Inverse(T;op;id;inv),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
grp: Group{i},
mon: Mon,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
inverse: Inverse(T;op;id;inv),
and: P ∧ Q
Lemmas referenced :
grp_wf,
grp_inv_wf,
grp_id_wf,
grp_op_wf,
grp_car_wf,
sq_stable__inverse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[g:Group\{i\}]. Inverse(|g|;*;e;\msim{})
Date html generated:
2016_05_15-PM-00_08_45
Last ObjectModification:
2016_01_15-PM-11_06_19
Theory : groups_1
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