### Nuprl Lemma : assert_of_rng_eq

`∀[r:DRng]. ∀[a,b:|r|].  uiff(↑(a =b b);a = b ∈ |r|)`

Proof

Definitions occuring in Statement :  drng: `DRng` rng_eq: `=b` rng_car: `|r|` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` infix_ap: `x f y` equal: `s = t ∈ T`
Definitions unfolded in proof :  eqfun_p: `IsEqFun(T;eq)` uall: `∀[x:A]. B[x]` member: `t ∈ T` and: `P ∧ Q` uiff: `uiff(P;Q)` uimplies: `b supposing a` prop: `ℙ` infix_ap: `x f y` drng: `DRng` implies: `P `` Q`
Lemmas referenced :  drng_all_properties assert_wf rng_eq_wf assert_witness equal_wf rng_car_wf drng_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis productElimination isect_memberEquality independent_pairEquality axiomEquality applyEquality setElimination rename equalityTransitivity equalitySymmetry independent_functionElimination

Latex:
\mforall{}[r:DRng].  \mforall{}[a,b:|r|].    uiff(\muparrow{}(a  =\msubb{}  b);a  =  b)

Date html generated: 2016_05_15-PM-00_20_38
Last ObjectModification: 2015_12_27-AM-00_02_46

Theory : rings_1

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