Nuprl Lemma : ocgrp_inverse
∀[g:OGrp]. ∀[x:|g|]. (((x * (~ x)) = e ∈ |g|) ∧ (((~ x) * x) = e ∈ |g|))
Proof
Definitions occuring in Statement :
ocgrp: OGrp,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
inverse: Inverse(T;op;id;inv),
and: P ∧ Q,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon
Lemmas referenced :
ocgrp_properties,
grp_car_wf,
ocgrp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality,
setElimination,
rename
Latex:
\mforall{}[g:OGrp]. \mforall{}[x:|g|]. (((x * (\msim{} x)) = e) \mwedge{} (((\msim{} x) * x) = e))
Date html generated:
2016_05_15-PM-00_13_12
Last ObjectModification:
2015_12_26-PM-11_41_59
Theory : groups_1
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