Nuprl Lemma : grp_op_cancel_r
∀[g:IGroup]. ∀[a,b,c:|g|]. a = b ∈ |g| supposing (a * c) = (b * 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_r,
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|]. a = b supposing (a * c) = (b * c)
Date html generated:
2017_10_01-AM-08_13_33
Last ObjectModification:
2017_02_28-PM-01_57_45
Theory : groups_1
Home
Index