Nuprl Lemma : permr_suptyping
∀T:Type. ∀Q:T ⟶ ℙ. ∀as,bs:{z:T| Q[z]} List. ((as ≡(T) bs) ⇒ (as ≡({z:T| Q[z]} ) bs))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
list: T List,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
permr: as ≡(T) bs,
cand: A c∧ B,
exists: ∃x:A. B[x],
sym_grp: Sym(n),
perm: Perm(T),
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,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
permr_wf,
subtype_rel_list,
subtype_rel_self,
istype-universe,
list_wf,
int_seg_wf,
length_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,
member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
isectElimination,
setEquality,
hypothesis,
sqequalRule,
instantiate,
universeEquality,
independent_isectElimination,
lambdaEquality_alt,
setElimination,
rename,
setIsType,
because_Cache,
inhabitedIsType,
functionIsType,
productElimination,
independent_pairFormation,
dependent_pairFormation_alt,
natural_numberEquality,
equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality_alt,
productIsType,
unionElimination,
applyLambdaEquality,
imageElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
hyp_replacement,
imageMemberEquality,
baseClosed
Latex:
\mforall{}T:Type. \mforall{}Q:T {}\mrightarrow{} \mBbbP{}. \mforall{}as,bs:\{z:T| Q[z]\} List. ((as \mequiv{}(T) bs) {}\mRightarrow{} (as \mequiv{}(\{z:T| Q[z]\} ) bs))
Date html generated:
2019_10_16-PM-01_00_20
Last ObjectModification:
2018_10_08-PM-05_45_39
Theory : perms_2
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