Nuprl Lemma : sd_ordered_cons_lemma
∀as,a,s:Top. (sd_ordered([a / as]) ~ before(a;as) ∧b sd_ordered(as))
Proof
Definitions occuring in Statement :
sd_ordered: sd_ordered(as),
before: before(u;ps),
cons: [a / b],
band: p ∧b q,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
sd_ordered: sd_ordered(as),
ycomb: Y,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
top_wf,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}as,a,s:Top. (sd\_ordered([a / as]) \msim{} before(a;as) \mwedge{}\msubb{} sd\_ordered(as))
Date html generated:
2016_05_16-AM-08_15_08
Last ObjectModification:
2015_12_28-PM-06_28_49
Theory : polynom_2
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