### 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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