Nuprl Lemma : accumulate_abort_cons_lemma
∀v,u,s,F:Top.
(accumulate_abort(x,y.F[x;y];s;[u / v]) ~ let s' ⟵ case s of inl(y) => F[u;y] | inr(_) => s
in accumulate_abort(x,y.F[x;y];s';v))
Proof
Definitions occuring in Statement :
accumulate_abort: accumulate_abort(x,sofar.F[x; sofar];s;L),
cons: [a / b],
callbyvalueall: callbyvalueall,
top: Top,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
accumulate_abort: accumulate_abort(x,sofar.F[x; sofar];s;L),
eager-accum: eager-accum(x,a.f[x; a];y;l),
cons: [a / b],
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
spread_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}v,u,s,F:Top.
(accumulate\_abort(x,y.F[x;y];s;[u / v]) \msim{} let s' \mleftarrow{}{} case s of inl(y) => F[u;y] | inr($_\mbackslash{}ff\000C7b}$) => s
in accumulate\_abort(x,y.F[x;y];s';v))
Date html generated:
2017_09_29-PM-05_51_42
Last ObjectModification:
2017_07_11-PM-02_30_27
Theory : omega
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