Nuprl Lemma : decide-simple-less
∀[a,b,c,d:Top].
(case if (a) < (b) then inl ⋅ else (inr ⋅ ) of inl() => c | inr() => d ~ if (a) < (b) then c else d)
Proof
Definitions occuring in Statement :
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
less: if (a) < (b) then c else d,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
inr: inr x ,
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
it: ⋅,
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],
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 :
lifting-strict-less,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf
Rules used in proof :
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,
isect_memberFormation,
sqequalAxiom,
isectEquality
Latex:
\mforall{}[a,b,c,d:Top].
(case if (a) < (b) then inl \mcdot{} else (inr \mcdot{} ) of inl() => c | inr() => d \msim{} if (a) < (b)
then c
else d)
Date html generated:
2017_10_01-AM-08_39_31
Last ObjectModification:
2017_07_26-PM-04_27_34
Theory : untyped!computation
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