Nuprl Lemma : lifting-strict-callbyvalueall
∀[F:Base]. ∀[p,q,r:Top].
∀[a,B:Top]. (F[let x ⟵ a in B[x];p;q;r] ~ let x ⟵ a in F[B[x];p;q;r]) supposing strict4(λx,y,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s],
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,
callbyvalueall: callbyvalueall,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
base_wf,
strict4_wf,
top_wf,
lifting-strict-callbyvalue
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
sqequalAxiom,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,B:Top]. (F[let x \mleftarrow{}{} a in B[x];p;q;r] \msim{} let x \mleftarrow{}{} a in F[B[x];p;q;r])
supposing strict4(\mlambda{}x,y,z,w. F[x;y;z;w])
Date html generated:
2016_05_13-PM-03_41_52
Last ObjectModification:
2016_01_14-PM-07_08_55
Theory : computation
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