Nuprl Lemma : sq_stable__is-simplex
∀k:ℕ. ∀L:ℝ^k List. SqStable(is-simplex(k;L)) supposing 0 < ||L||
Proof
Definitions occuring in Statement :
is-simplex: is-simplex(k;L),
real-vec: ℝ^n,
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
sq_stable: SqStable(P),
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
is-simplex: is-simplex(k;L),
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T
Lemmas referenced :
member-less_than,
length_wf,
real-vec_wf,
sq_stable__real-vec-free,
map_wf,
real-vec-sub_wf,
hd_wf,
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,
istype-le,
intformless_wf,
int_formula_prop_less_lemma,
tl_wf,
istype-less_than,
list_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
rename,
dependent_functionElimination,
because_Cache,
lambdaEquality_alt,
setElimination,
dependent_set_memberEquality_alt,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
imageElimination,
productElimination
Latex:
\mforall{}k:\mBbbN{}. \mforall{}L:\mBbbR{}\^{}k List. SqStable(is-simplex(k;L)) supposing 0 < ||L||
Date html generated:
2019_10_30-AM-08_47_00
Last ObjectModification:
2019_09_18-PM-02_03_15
Theory : reals
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