Nuprl Lemma : 0-dim-complex-polyhedron-decidable
∀k:ℕ. ∀K:0-dim-complex. ∀x,y:|K|. Dec(x ≡ y)
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
rn-prod-metric: rn-prod-metric(n),
meq: x ≡ y,
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x],
natural_number: $n,
rational-cube-complex: n-dim-complex
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
req-vec: req-vec(n;x;y),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
pi1: fst(t),
rational-interval: ℚInterval,
rational-cube: ℚCube(k),
prop: ℙ,
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
lelt: i ≤ j < k,
int_seg: {i..j-},
rational-cube-complex: n-dim-complex,
real-vec: ℝ^n,
exists: ∃x:A. B[x],
stable-union: Error :stable-union,
rat-cube-complex-polyhedron: |K|,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
req-rat2real,
decidable__equal_rationals,
rationals_wf,
equal_wf,
req_wf,
decidable__all_int_seg,
meq-rn-prod-metric,
iff_weakening_uiff,
decidable_functionality,
rational-interval_wf,
int_seg_wf,
subtype_rel_self,
int_formula_prop_less_lemma,
intformless_wf,
length_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
rational-cube_wf,
select_wf,
rat2real_wf,
req-vec_functionality,
req-vec_wf,
real-vec_wf,
metric-on-subtype,
rn-prod-metric_wf,
meq_wf,
istype-nat,
rational-cube-complex_wf,
istype-le,
istype-void,
rat-cube-complex-polyhedron_wf,
0-dim-complex-polyhedron
Rules used in proof :
instantiate,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
inhabitedIsType,
functionEquality,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
unionElimination,
imageElimination,
productElimination,
rename,
setElimination,
lambdaEquality_alt,
independent_isectElimination,
applyEquality,
voidElimination,
sqequalRule,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality_alt,
isectElimination,
universeIsType,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}k:\mBbbN{}. \mforall{}K:0-dim-complex. \mforall{}x,y:|K|. Dec(x \mequiv{} y)
Date html generated:
2019_10_30-AM-10_13_22
Last ObjectModification:
2019_10_28-PM-02_18_44
Theory : real!vectors
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