Nuprl Lemma : rng_plus_cancel_l
∀[r:Rng]. ∀[a,b,c:|r|]. b = c ∈ |r| supposing (a +r b) = (a +r c) ∈ |r|
Proof
Definitions occuring in Statement :
rng: Rng,
rng_plus: +r,
rng_car: |r|,
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,
subtype_rel: A ⊆r B,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
uimplies: b supposing a,
prop: ℙ,
rng: Rng,
infix_ap: x f y
Lemmas referenced :
grp_op_cancel_l,
add_grp_of_rng_wf_a,
grp_subtype_igrp,
equal_wf,
rng_car_wf,
rng_plus_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:Rng]. \mforall{}[a,b,c:|r|]. b = c supposing (a +r b) = (a +r c)
Date html generated:
2016_05_15-PM-00_21_25
Last ObjectModification:
2015_12_27-AM-00_02_12
Theory : rings_1
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