### Nuprl Lemma : ring_triv

`∀[r:Rng]. ∀[a:|r|]. (a = 0 ∈ |r|) supposing 1 = 0 ∈ |r|`

Proof

Definitions occuring in Statement :  rng: `Rng` rng_one: `1` rng_zero: `0` rng_car: `|r|` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` rng: `Rng` prop: `ℙ` squash: `↓T` and: `P ∧ Q` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` implies: `P `` Q`
Lemmas referenced :  rng_car_wf equal_wf rng_one_wf rng_zero_wf rng_wf infix_ap_wf rng_times_wf squash_wf true_wf rng_times_zero rng_times_one 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 sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry applyLambdaEquality applyEquality lambdaEquality imageElimination universeEquality productElimination natural_numberEquality imageMemberEquality baseClosed independent_isectElimination independent_functionElimination

Latex:
\mforall{}[r:Rng].  \mforall{}[a:|r|].  (a  =  0)  supposing  1  =  0

Date html generated: 2017_10_01-AM-08_17_31
Last ObjectModification: 2017_02_28-PM-02_02_39

Theory : rings_1

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