Nuprl Lemma : lapp_mon_wf
∀s:DSet. (<s List, @> ∈ Mon)
Proof
Definitions occuring in Statement :
lapp_mon: <s List, @>,
all: ∀x:A. B[x],
member: t ∈ T,
mon: Mon,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
lapp_mon: <s List, @>,
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
top: Top,
ident: Ident(T;op;id),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
mk_mon,
list_wf,
set_car_wf,
eq_list_wf,
btrue_wf,
append_wf,
nil_wf,
dset_wf,
append_assoc,
list_ind_nil_lemma,
append_back_nil
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation_alt,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
independent_pairFormation,
productElimination,
independent_pairEquality
Latex:
\mforall{}s:DSet. (<s List, @> \mmember{} Mon)
Date html generated:
2019_10_16-PM-01_03_04
Last ObjectModification:
2018_09_26-PM-08_14_32
Theory : list_2
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