Nuprl Lemma : geometric-simplex_wf
∀[k,n:ℕ]. (geometric-simplex(k;n) ∈ Type)
Proof
Definitions occuring in Statement :
geometric-simplex: geometric-simplex(k;n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geometric-simplex: geometric-simplex(k;n),
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
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
Lemmas referenced :
list_wf,
real-vec_wf,
equal-wf-base,
is-simplex_wf,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
axiomEquality,
inhabitedIsType,
isectIsTypeImplies
Latex:
\mforall{}[k,n:\mBbbN{}]. (geometric-simplex(k;n) \mmember{} Type)
Date html generated:
2019_10_30-AM-08_47_56
Last ObjectModification:
2019_09_18-PM-02_06_12
Theory : reals
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