Nuprl Lemma : band_bor_distributive
∀[a,b,c:Top]. (a ∧b (b ∨bc) ~ (a ∧b b) ∨b(a ∧b c))
Proof
Definitions occuring in Statement :
bor: p ∨bq,
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bor: p ∨bq,
btrue: tt,
it: ⋅,
bfalse: ff,
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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓
Lemmas referenced :
lifting-strict-decide,
istype-void,
strict4-decide,
has-value_wf_base,
is-exception_wf,
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,
hypothesisEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
because_Cache,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
unionElimination,
sqleReflexivity,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
axiomSqEquality,
Error :universeIsType
Latex:
\mforall{}[a,b,c:Top]. (a \mwedge{}\msubb{} (b \mvee{}\msubb{}c) \msim{} (a \mwedge{}\msubb{} b) \mvee{}\msubb{}(a \mwedge{}\msubb{} c))
Date html generated:
2019_06_20-PM-01_04_47
Last ObjectModification:
2019_06_20-PM-01_01_01
Theory : bool_1
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