Nuprl Lemma : lifting-callbyvalueall-int_eq
∀[a,b,c,d,H:Top].  (let x ⟵ if a=b  then c  else d in H[x] ~ if a=b  then let x ⟵ c in H[x]  else let x ⟵ d in H[x])
Proof
Definitions occuring in Statement : 
callbyvalueall: callbyvalueall, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
int_eq: if a=b  then c  else d
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
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
, 
strict4: strict4(F)
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
callbyvalueall: callbyvalueall, 
evalall: evalall(t)
, 
guard: {T}
, 
or: P ∨ Q
, 
has-value: (a)↓
, 
squash: ↓T
Lemmas referenced : 
top_wf, 
is-exception-evalall, 
is-exception_wf, 
base_wf, 
has-value_wf_base, 
has-valueall-has-value, 
has-valueall-if-has-value-callbyvalueall, 
lifting-strict-int_eq
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
baseClosed, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
hypothesisEquality, 
baseApply, 
closedConclusion, 
hypothesis, 
callbyvalueExceptionCases, 
inrFormation, 
callbyvalueCallbyvalue, 
callbyvalueReduce, 
imageMemberEquality, 
imageElimination, 
independent_functionElimination, 
sqequalAxiom, 
because_Cache
Latex:
\mforall{}[a,b,c,d,H:Top].
    (let  x  \mleftarrow{}{}  if  a=b    then  c    else  d
      in  H[x]  \msim{}  if  a=b    then  let  x  \mleftarrow{}{}  c  in  H[x]    else  let  x  \mleftarrow{}{}  d  in  H[x])
Date html generated:
2016_05_13-PM-03_42_29
Last ObjectModification:
2016_01_14-PM-07_08_29
Theory : computation
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