Nuprl Lemma : rng_when_when
∀[r:Rng]. ∀[b,b':𝔹]. ∀[p:|r|]. ((when b. when b'. p) = (when b ∧b b'. p) ∈ |r|)
Proof
Definitions occuring in Statement :
rng_when: rng_when,
rng: Rng,
rng_car: |r|,
band: p ∧b q,
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_when,
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 \mwedge{}\msubb{} b'. p))
Date html generated:
2016_05_15-PM-00_29_12
Last ObjectModification:
2015_12_26-PM-11_58_18
Theory : rings_1
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