Nuprl Lemma : cons_permr_mem
∀s:DSet. ∀a:|s|. ∀as,bs:|s| List. (([a / as] ≡(|s|) bs) ⇒ (↑(a ∈b bs)))
Proof
Definitions occuring in Statement :
mem: a ∈b as,
permr: as ≡(T) bs,
cons: [a / b],
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
prop: ℙ,
permr: as ≡(T) bs,
cand: A c∧ B,
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
sym_grp: Sym(n),
perm: Perm(T),
select: L[n],
cons: [a / b],
guard: {T}
Lemmas referenced :
permr_wf,
set_car_wf,
cons_wf,
list_wf,
dset_wf,
permr_inversion,
mem_iff_exists,
istype-false,
length_of_cons_lemma,
istype-void,
non_neg_length,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
intformeq_wf,
itermAdd_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
le_wf,
less_than_wf,
length_wf,
perm_f_wf,
int_seg_wf,
select_wf,
int_seg_properties,
decidable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
inhabitedIsType,
independent_functionElimination,
productElimination,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
isect_memberEquality_alt,
voidElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
independent_isectElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
productIsType,
applyEquality,
equalityIsType1
Latex:
\mforall{}s:DSet. \mforall{}a:|s|. \mforall{}as,bs:|s| List. (([a / as] \mequiv{}(|s|) bs) {}\mRightarrow{} (\muparrow{}(a \mmember{}\msubb{} bs)))
Date html generated:
2019_10_16-PM-01_03_37
Last ObjectModification:
2018_10_08-PM-01_00_55
Theory : list_2
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