Nuprl Lemma : callbyvalueall-reduce-repeat-right-branch
∀[a,d,F,G:Top].
(let x ⟵ a
in case d[x] of inl(u) => F[x;u] | inr(v) => let y ⟵ x in G[y;v] ~ let x ⟵ a
in case d[x]
of inl(u) =>
F[x;u]
| inr(v) =>
G[x;v])
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
prop: ℙ,
has-value: (a)↓
Lemmas referenced :
top_wf,
evalall-sqequal,
has-valueall_wf_base,
cbv_sqequal
Rules used in proof :
cut,
sqequalRule,
thin,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
hypothesis,
because_Cache,
callbyvalueReduce,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[a,d,F,G:Top].
(let x \mleftarrow{}{} a
in case d[x] of inl(u) => F[x;u] | inr(v) => let y \mleftarrow{}{} x in G[y;v] \msim{} let x \mleftarrow{}{} a
in case d[x]
of inl(u) =>
F[x;u]
| inr(v) =>
G[x;v])
Date html generated:
2016_05_15-PM-02_08_41
Last ObjectModification:
2016_01_15-PM-10_21_48
Theory : untyped!computation
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