Nuprl Lemma : test-lifting
∀x:Top. (if isl(x) then 1 + outl(x) else 2 fi ~ case x of inl(y) => 1 + y | inr(z) => 2)
Proof
Definitions occuring in Statement :
outl: outl(x),
ifthenelse: if b then t else f fi ,
isl: isl(x),
top: Top,
all: ∀x:A. B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
ifthenelse: if b then t else f fi ,
isl: isl(x),
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,
btrue: tt,
outl: outl(x),
strict4: strict4(F),
and: P ∧ Q,
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
false: False,
bfalse: ff
Lemmas referenced :
lifting-strict-decide,
istype-void,
strict4-decide,
value-type-has-value,
int-value-type,
has-value_wf_base,
istype-base,
exception-not-value,
is-exception_wf,
strictness-add-right,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
hypothesis,
independent_isectElimination,
independent_pairFormation,
callbyvalueAdd,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
intEquality,
because_Cache,
Error :universeIsType,
addExceptionCases,
exceptionSqequal,
Error :inlFormation_alt,
imageMemberEquality,
imageElimination,
sqleReflexivity,
independent_functionElimination,
Error :inhabitedIsType,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
unionElimination,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
decideExceptionCases,
axiomSqleEquality
Latex:
\mforall{}x:Top. (if isl(x) then 1 + outl(x) else 2 fi \msim{} case x of inl(y) => 1 + y | inr(z) => 2)
Date html generated:
2019_06_20-PM-01_04_37
Last ObjectModification:
2019_06_20-PM-01_01_30
Theory : computation
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