Nuprl Lemma : grp_inverse
∀[g:IGroup]. ∀[a:|g|]. (((a * (~ a)) = e ∈ |g|) ∧ (((~ a) * a) = e ∈ |g|))
Proof
Definitions occuring in Statement :
igrp: IGroup,
grp_inv: ~,
grp_id: e,
grp_op: *,
grp_car: |g|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
and: P ∧ Q,
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
inverse: Inverse(T;op;id;inv),
uall: ∀[x:A]. B[x],
member: t ∈ T,
igrp: IGroup,
and: P ∧ Q,
imon: IMonoid
Lemmas referenced :
igrp_properties,
grp_car_wf,
igrp_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[g:IGroup]. \mforall{}[a:|g|]. (((a * (\msim{} a)) = e) \mwedge{} (((\msim{} a) * a) = e))
Date html generated:
2016_05_15-PM-00_08_02
Last ObjectModification:
2015_12_26-PM-11_46_07
Theory : groups_1
Home
Index