Nuprl Lemma : assert_of_bpermr
∀s:DSet. ∀as,bs:|s| List. (↑(as ≡b bs) ⇐⇒ as ≡(|s|) bs)
Proof
Definitions occuring in Statement :
bpermr: as ≡b bs,
permr: as ≡(T) bs,
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
bpermr: as ≡b bs,
ycomb: Y,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cons: [a / b],
bfalse: ff,
false: False,
not: ¬A,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
band: p ∧b q,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
cand: A c∧ B
Lemmas referenced :
list_wf,
set_car_wf,
dset_wf,
list_induction,
all_wf,
iff_wf,
assert_wf,
bpermr_wf,
permr_wf,
list_ind_nil_lemma,
istype-void,
list_ind_cons_lemma,
list-cases,
null_nil_lemma,
permr_reflex,
nil_wf,
true_wf,
product_subtype_list,
null_cons_lemma,
cons_wf,
permr_inversion,
not_permr_cons_nil,
remove1_wf,
iff_weakening_uiff,
mem_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
bfalse_wf,
assert_of_band,
permr_functionality_wrt_permr,
permr_transitivity,
cons_functionality_wrt_permr,
cons_remove1_permr,
permr_weakening,
cons_permr_mem,
permr_hd_cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality_alt,
applyEquality,
dependent_functionElimination,
because_Cache,
inhabitedIsType,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination,
functionIsType,
productIsType,
unionElimination,
independent_pairFormation,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIsType1,
instantiate,
cumulativity,
productEquality
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. (\muparrow{}(as \mequiv{}\msubb{} bs) \mLeftarrow{}{}\mRightarrow{} as \mequiv{}(|s|) bs)
Date html generated:
2019_10_16-PM-01_03_59
Last ObjectModification:
2018_10_08-AM-11_12_23
Theory : list_2
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