Nuprl Lemma : mon_when_when
∀[g:Mon]. ∀[b,b':𝔹]. ∀[p:|g|]. ((when b. when b'. p) = (when b ∧b b'. p) ∈ |g|)
Proof
Definitions occuring in Statement :
mon_when: when b. p,
mon: Mon,
grp_car: |g|,
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,
mon_when: when b. p,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
bfalse: ff,
mon: Mon
Lemmas referenced :
grp_id_wf,
grp_car_wf,
bool_wf,
mon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
sqequalRule,
hypothesisEquality,
lemma_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[g:Mon]. \mforall{}[b,b':\mBbbB{}]. \mforall{}[p:|g|]. ((when b. when b'. p) = (when b \mwedge{}\msubb{} b'. p))
Date html generated:
2016_05_15-PM-00_18_50
Last ObjectModification:
2015_12_26-PM-11_37_57
Theory : groups_1
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