Nuprl Lemma : fpf-conversion-test
4 : 2 ⊕ 6 : 2 ⊕ 7 : 5 = <[4; 6; 7], λx.if x ∈b [4; 6] then 2 else 5 fi > ∈ i:ℤ fp-> ℤ
Proof
Definitions occuring in Statement : 
fpf-single: x : v
, 
fpf-join: f ⊕ g
, 
fpf: a:A fp-> B[a]
, 
deq-member: x ∈b L
, 
cons: [a / b]
, 
nil: []
, 
int-deq: IntDeq
, 
ifthenelse: if b then t else f fi 
, 
lambda: λx.A[x]
, 
pair: <a, b>
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
cons: [a / b]
, 
nil: []
, 
it: ⋅
, 
ifthenelse: if b then t else f fi 
, 
deq-member: x ∈b L
, 
reduce: reduce(f;k;as)
, 
list_ind: list_ind, 
bor: p ∨bq
, 
int-deq: IntDeq
, 
eq_int: (i =z j)
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w])
, 
member: t ∈ T
, 
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
, 
has-value: (a)↓
, 
prop: ℙ
, 
guard: {T}
, 
or: P ∨ Q
, 
squash: ↓T
, 
btrue: tt
, 
bfalse: ff
, 
fpf-join: f ⊕ g
, 
append: as @ bs
, 
pi1: fst(t)
, 
fpf-single: x : v
, 
filter: filter(P;l)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
bnot: ¬bb
, 
fpf-dom: x ∈ dom(f)
, 
fpf-cap: f(x)?z
, 
fpf-ap: f(x)
, 
pi2: snd(t)
Lemmas referenced : 
lifting-strict-int_eq, 
top_wf, 
equal_wf, 
has-value_wf_base, 
base_wf, 
is-exception_wf, 
lifting-strict-spread, 
lifting-strict-callbyvalue, 
lifting-strict-ispair, 
lifting-strict-decide, 
lifting-strict-isaxiom, 
fpf-join_wf, 
fpf-single_wf, 
int-deq_wf
Rules used in proof : 
comment, 
sqequalSubstitution, 
sqequalRule, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
baseClosed, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
callbyvalueDecide, 
hypothesis, 
hypothesisEquality, 
equalityTransitivity, 
equalitySymmetry, 
unionEquality, 
unionElimination, 
sqleReflexivity, 
dependent_functionElimination, 
independent_functionElimination, 
baseApply, 
closedConclusion, 
decideExceptionCases, 
inrFormation, 
because_Cache, 
imageMemberEquality, 
imageElimination, 
exceptionSqequal, 
inlFormation, 
instantiate, 
callbyvalueCallbyvalue, 
callbyvalueReduce, 
callbyvalueExceptionCases, 
callbyvalueApply, 
applyExceptionCases, 
intEquality, 
lambdaEquality, 
natural_numberEquality
Latex:
4  :  2  \moplus{}  6  :  2  \moplus{}  7  :  5  =  <[4;  6;  7],  \mlambda{}x.if  x  \mmember{}\msubb{}  [4;  6]  then  2  else  5  fi  >
Date html generated:
2018_05_21-PM-09_25_16
Last ObjectModification:
2018_02_09-AM-10_21_00
Theory : finite!partial!functions
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