Nuprl Lemma : distinct_wf
∀s:DSet. ∀ps:|s| List. (distinct{s}(ps) ∈ 𝔹)
Proof
Definitions occuring in Statement :
distinct: distinct{s}(ps),
list: T List,
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
distinct: distinct{s}(ps),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_apply: x[s1;s2]
Lemmas referenced :
mon_htfor_wf,
band_mon_wf,
set_car_wf,
ball_wf,
bnot_wf,
infix_ap_wf,
bool_wf,
set_eq_wf,
list_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
because_Cache,
isectElimination,
setElimination,
rename,
hypothesisEquality,
lambdaEquality
Latex:
\mforall{}s:DSet. \mforall{}ps:|s| List. (distinct\{s\}(ps) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-07_37_23
Last ObjectModification:
2015_12_28-PM-05_45_27
Theory : list_2
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