Nuprl Lemma : sq_stable__real-vec-free
∀k:ℕ. ∀L:ℝ^k List. SqStable(real-vec-free(k;L))
Proof
Definitions occuring in Statement :
real-vec-free: real-vec-free(k;L),
real-vec: ℝ^n,
list: T List,
nat: ℕ,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
real-vec-free: real-vec-free(k;L),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
less_than: a < b,
squash: ↓T,
real-vec-sep: a ≠ b,
rless: x < y,
sq_exists: ∃x:A [B[x]],
subtype_rel: A ⊆r B,
real: ℝ,
sq_stable: SqStable(P),
nat_plus: ℕ+,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
uiff: uiff(P;Q),
so_apply: x[s]
Lemmas referenced :
sq_stable__all,
int_seg_wf,
length_wf,
real-vec_wf,
real_wf,
real-vec-sep_wf,
length_wf_nat,
int-to-real_wf,
real-vec-sum_wf,
subtract_wf,
real-vec-mul_wf,
select_wf,
int_seg_properties,
sq_stable__less_than,
real-vec-dist_wf,
nat_plus_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
istype-le,
add-is-int-iff,
subtract-is-int-iff,
intformless_wf,
itermAdd_wf,
itermSubtract_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_subtract_lemma,
false_wf,
istype-less_than,
sq_stable__real-vec-sep,
list_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
setElimination,
rename,
productElimination,
universeIsType,
because_Cache,
closedConclusion,
independent_isectElimination,
imageElimination,
addEquality,
applyEquality,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
dependent_set_memberEquality_alt,
pointwiseFunctionality,
promote_hyp,
baseApply,
productIsType,
functionIsType
Latex:
\mforall{}k:\mBbbN{}. \mforall{}L:\mBbbR{}\^{}k List. SqStable(real-vec-free(k;L))
Date html generated:
2019_10_30-AM-08_45_37
Last ObjectModification:
2019_09_18-PM-01_57_50
Theory : reals
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