Nuprl Lemma : reduce-ifthenelse
∀[f,k,x,y,b:Top]. (reduce(f;k;if b then x else y fi ) ~ if b then reduce(f;k;x) else reduce(f;k;y) fi )
Proof
Definitions occuring in Statement :
reduce: reduce(f;k;as),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reduce: reduce(f;k;as),
list_ind: list_ind,
ifthenelse: if b then t else f fi ,
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,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T
Lemmas referenced :
top_wf,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-decide
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,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[f,k,x,y,b:Top].
(reduce(f;k;if b then x else y fi ) \msim{} if b then reduce(f;k;x) else reduce(f;k;y) fi )
Date html generated:
2016_05_14-AM-06_29_32
Last ObjectModification:
2016_01_14-PM-08_25_36
Theory : list_0
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