Nuprl Lemma : bnot_bnot
∀[p:Top]. (¬b¬bp ~ p ∧b tt)
Proof
Definitions occuring in Statement :
band: p ∧b q,
bnot: ¬bb,
btrue: tt,
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,
btrue: tt
Lemmas referenced :
lifting-strict-decide,
strict4-decide,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis,
sqequalAxiom
Latex:
\mforall{}[p:Top]. (\mneg{}\msubb{}\mneg{}\msubb{}p \msim{} p \mwedge{}\msubb{} tt)
Date html generated:
2018_05_21-PM-00_03_33
Last ObjectModification:
2018_05_19-AM-07_10_48
Theory : bool_1
Home
Index