### Nuprl Lemma : rng_when_swap

`∀[r:Rng]. ∀[b,b':𝔹]. ∀[p:|r|].  ((when b. when b'. p) = (when b'. when b. p) ∈ |r|)`

Proof

Definitions occuring in Statement :  rng_when: rng_when rng: `Rng` rng_car: `|r|` bool: `𝔹` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` grp: `Group{i}` rng_when: rng_when add_grp_of_rng: `r↓+gp` grp_car: `|g|` pi1: `fst(t)` rng: `Rng`
Lemmas referenced :  mon_when_swap add_grp_of_rng_wf_a grp_wf rng_car_wf bool_wf rng_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis applyEquality lambdaEquality setElimination rename sqequalRule isect_memberEquality axiomEquality

Latex:
\mforall{}[r:Rng].  \mforall{}[b,b':\mBbbB{}].  \mforall{}[p:|r|].    ((when  b.  when  b'.  p)  =  (when  b'.  when  b.  p))

Date html generated: 2016_05_15-PM-00_29_16
Last ObjectModification: 2015_12_26-PM-11_58_13

Theory : rings_1

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