Nuprl Lemma : grp_op_cancel_l
∀[g:IGroup]. ∀[a,b,c:|g|].  b = c ∈ |g| supposing (a * b) = (a * c) ∈ |g|
Proof
Definitions occuring in Statement : 
igrp: IGroup
, 
grp_op: *
, 
grp_car: |g|
, 
uimplies: b supposing a
, 
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
, 
uimplies: b supposing a
, 
prop: ℙ
, 
igrp: IGroup
, 
imon: IMonoid
, 
infix_ap: x f y
, 
squash: ↓T
, 
true: True
, 
subtype_rel: A ⊆r B
, 
and: P ∧ Q
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
equal_wf, 
grp_car_wf, 
grp_op_wf, 
igrp_wf, 
grp_op_l, 
grp_inv_wf, 
squash_wf, 
true_wf, 
mon_assoc, 
grp_inverse, 
mon_ident, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
setElimination, 
rename, 
hypothesisEquality, 
applyEquality, 
because_Cache, 
sqequalRule, 
isect_memberEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
lambdaEquality, 
imageElimination, 
universeEquality, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
productElimination, 
independent_functionElimination
Latex:
\mforall{}[g:IGroup].  \mforall{}[a,b,c:|g|].    b  =  c  supposing  (a  *  b)  =  (a  *  c)
Date html generated:
2017_10_01-AM-08_13_30
Last ObjectModification:
2017_02_28-PM-01_57_47
Theory : groups_1
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