Nuprl Lemma : permr_upto_wf
∀T:Type. ∀R:T ⟶ T ⟶ ℙ. ∀as,bs:T List. (as ≡ bs upto x,y.R[x;y] ∈ ℙ)
Proof
Definitions occuring in Statement :
permr_upto: as ≡ bs upto x,y.R[x; y] ,
list: T List,
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
permr_upto: as ≡ bs upto x,y.R[x; y] ,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
sym_grp: Sym(n),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
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,
false: False,
nat: ℕ,
less_than: a < b,
squash: ↓T,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
equal_wf,
length_wf,
exists_wf,
perm_wf,
int_seg_wf,
all_wf,
select_wf,
perm_f_wf,
non_neg_length,
int_seg_properties,
decidable__le,
le_wf,
less_than_wf,
length_wf_nat,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
cut,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
lambdaEquality_alt,
applyEquality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_set_memberEquality_alt,
independent_pairFormation,
productIsType,
universeIsType,
unionElimination,
applyLambdaEquality,
imageElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
inhabitedIsType,
functionIsType,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}. \mforall{}as,bs:T List. (as \mequiv{} bs upto x,y.R[x;y] \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-01_01_08
Last ObjectModification:
2018_10_08-AM-10_05_54
Theory : perms_2
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