Nuprl Lemma : bnot_thru_bor
∀[p,q:Top]. (¬b(p ∨bq) ~ (¬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 ,
bor: p ∨bq,
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,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
btrue: tt,
bfalse: ff,
it: ⋅,
band: p ∧b q
Lemmas referenced :
lifting-strict-decide,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_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,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesis,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom
Latex:
\mforall{}[p,q:Top]. (\mneg{}\msubb{}(p \mvee{}\msubb{}q) \msim{} (\mneg{}\msubb{}p) \mwedge{}\msubb{} (\mneg{}\msubb{}q))
Date html generated:
2017_04_14-AM-07_29_52
Last ObjectModification:
2017_02_27-PM-02_58_30
Theory : bool_1
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