Nuprl Lemma : grp_eq_op_r
∀[g:IGroup]. ∀[a,b,c:|g|]. uiff(a = b ∈ |g|;(a * c) = (b * c) ∈ |g|)
Proof
Definitions occuring in Statement :
igrp: IGroup,
grp_op: *,
grp_car: |g|,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
igrp: IGroup,
imon: IMonoid,
infix_ap: x f y
Lemmas referenced :
equal_wf,
grp_car_wf,
grp_op_wf,
igrp_wf,
grp_op_r,
grp_op_cancel_r
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
applyEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[g:IGroup]. \mforall{}[a,b,c:|g|]. uiff(a = b;(a * c) = (b * c))
Date html generated:
2016_05_15-PM-00_08_25
Last ObjectModification:
2015_12_26-PM-11_45_52
Theory : groups_1
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