Nuprl Lemma : test-cbva-normalize
∀[a,B:Top]. (let x ⟵ a in <let y ⟵ x in B[y], let z ⟵ a in B[z] + 22, eval w = a in B[w] + 3 + 1> ~ let x ⟵ a in <B\000C[x], B[x] + 22, (B[x] + 3) + 1>)
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
callbyvalue: callbyvalue,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
pair: <a, b>,
add: n + m,
natural_number: $n,
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,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
top_wf,
has-valueall_wf_base,
has-valueall-has-value,
evalall-sqequal,
cbv_sqequal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
sqequalTransitivity,
computationStep,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
hypothesis,
callbyvalueReduce,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[a,B:Top]. (let x \mleftarrow{}{} a in <let y \mleftarrow{}{} x in B[y], let z \mleftarrow{}{} a in B[z] + 22, eval w = a in B[w] + 3 + 1\000C> \msim{} let x \mleftarrow{}{} a in <B[x], B[x] + 22, (B[x] + 3) + 1>)
Date html generated:
2016_05_13-PM-04_08_00
Last ObjectModification:
2016_01_14-PM-07_45_54
Theory : fun_1
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