Nuprl Lemma : lifting-strict-ifthenelse
∀[F:Base]. ∀[p,q,r:Top].
∀[a,A,B:Top]. (F[if a then A else B fi ;p;q;r] ~ if a then F[A;p;q;r] else F[B;p;q;r] fi )
supposing strict4(λx,y,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
lambda: λx.A[x],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
ifthenelse: if b then t else f fi ,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
lifting-strict-decide,
base_wf,
strict4_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,A,B:Top]. (F[if a then A else B fi ;p;q;r] \msim{} if a then F[A;p;q;r] else F[B;p;q;r] fi )
supposing strict4(\mlambda{}x,y,z,w. F[x;y;z;w])
Date html generated:
2016_05_13-PM-03_41_54
Last ObjectModification:
2016_01_14-PM-07_08_57
Theory : computation
Home
Index