Nuprl Lemma : lifting-strict-decide
∀[F:Base]. ∀[p,q,r:Top].
∀[a,A,B:Top].
(F[case a of inl(x) => A[x] | inr(x) => B[x];p;q;r] ~ case a of inl(x) => F[A[x];p;q;r] | inr(x) => F[B[x];p;q;r])
supposing strict4(λx,y,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s],
lambda: λx.A[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
squash: ↓T,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Lemmas referenced :
top_wf,
equal_wf,
injection-eta,
isl_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
has-value_wf_base,
is-exception_wf,
eqff_to_assert,
assert_of_bnot,
strict4_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
sqequalHypSubstitution,
sqequalRule,
productElimination,
hypothesis,
dependent_functionElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_functionElimination,
callbyvalueDecide,
equalityTransitivity,
equalitySymmetry,
unionEquality,
extract_by_obid,
lambdaFormation,
unionElimination,
sqleReflexivity,
isectElimination,
imageElimination,
axiomSqleEquality,
decideExceptionCases,
exceptionSqequal,
because_Cache,
instantiate,
cumulativity,
independent_isectElimination,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,A,B:Top].
(F[case a of inl(x) => A[x] | inr(x) => B[x];p;q;r] \msim{} case a
of inl(x) =>
F[A[x];p;q;r]
| inr(x) =>
F[B[x];p;q;r])
supposing strict4(\mlambda{}x,y,z,w. F[x;y;z;w])
Date html generated:
2017_04_14-AM-07_20_51
Last ObjectModification:
2017_02_27-PM-02_54_23
Theory : computation
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