Nuprl Lemma : bnot_thru_band
∀[p,q:Top]. (¬b(p ∧b q) ~ (¬bp) ∨b(¬bq))
Proof
Definitions occuring in Statement :
bor: p ∨bq,
band: p ∧b q,
bnot: ¬bb,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
bfalse: ff,
it: ⋅,
btrue: tt,
bor: p ∨bq
Lemmas referenced :
lifting-strict-decide,
istype-void,
strict4-decide,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
hypothesis,
independent_isectElimination,
axiomSqEquality,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType
Latex:
\mforall{}[p,q:Top]. (\mneg{}\msubb{}(p \mwedge{}\msubb{} q) \msim{} (\mneg{}\msubb{}p) \mvee{}\msubb{}(\mneg{}\msubb{}q))
Date html generated:
2019_06_20-PM-01_04_48
Last ObjectModification:
2019_06_20-PM-01_00_55
Theory : bool_1
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