Nuprl Lemma : permr_weakening
∀T:Type. ∀as,bs:T List. ((as = bs ∈ (T List)) ⇒ (as ≡(T) bs))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
permr: as ≡(T) bs,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
true: True,
prop: ℙ,
exists: ∃x:A. B[x],
sym_grp: Sym(n),
so_lambda: λ2x.t[x],
perm: Perm(T),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
ge: i ≥ j ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
so_apply: x[s],
id_perm: id_perm(),
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
identity: Id
Lemmas referenced :
less_than_wf,
and_wf,
squash_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
le_wf,
nat_properties,
length_wf_nat,
lelt_wf,
decidable__le,
int_seg_properties,
non_neg_length,
perm_f_wf,
select_wf,
all_wf,
int_seg_wf,
id_perm_wf,
list_wf,
equal_wf,
length_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_pairFormation,
dependent_pairFormation,
dependent_functionElimination,
equalityTransitivity,
cumulativity,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_set_memberEquality,
unionElimination,
setEquality,
intEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}as,bs:T List. ((as = bs) {}\mRightarrow{} (as \mequiv{}(T) bs))
Date html generated:
2016_05_16-AM-07_32_31
Last ObjectModification:
2016_01_16-PM-11_09_33
Theory : perms_2
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