Nuprl Lemma : lifting-isaxiom-decide
∀[a,b,c,F,G:Top].
(if case a of inl(x) => F[x] | inr(x) => G[x] = Ax then b otherwise c ~ case a
of inl(x) =>
if F[x] = Ax then b otherwise c
| inr(x) =>
if G[x] = Ax then b otherwise c)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
isaxiom: if z = Ax then a otherwise b,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
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],
top: Top,
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,
so_lambda: λ2x.t[x],
so_apply: x[s]
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,
callbyvalueIsaxiom,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
isaxiomExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b,c,F,G:Top].
(if case a of inl(x) => F[x] | inr(x) => G[x] = Ax then b otherwise c \msim{} case a
of inl(x) =>
if F[x] = Ax then b otherwise c
| inr(x) =>
if G[x] = Ax then b otherwise c)
Date html generated:
2016_05_13-PM-03_42_18
Last ObjectModification:
2016_01_14-PM-07_08_43
Theory : computation
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