Nuprl Lemma : face-complex_wf
∀[k:ℕ]. ∀[n:ℕ+]. ∀[K:n-dim-complex]. (face-complex(k;K) ∈ n - 1-dim-complex)
Proof
Definitions occuring in Statement :
face-complex: face-complex(k;L),
rational-cube-complex: n-dim-complex,
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
true: True,
l_member: (x ∈ l),
guard: {T},
squash: ↓T,
sq_stable: SqStable(P),
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
nat_plus: ℕ+,
so_apply: x[s],
nat: ℕ,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
exists: ∃x:A. B[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
so_apply: x[s1;s2],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
cand: A c∧ B,
rational-cube-complex: n-dim-complex,
bfalse: ff,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
face-complex: face-complex(k;L),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
select_wf,
iff_weakening_equal,
subtype_rel_self,
istype-universe,
true_wf,
squash_wf,
equal_wf,
subtract_wf,
rat-cube-face_wf,
subtype_rel_list,
faces-of-compatible-rat-cubes,
sq_stable__compatible-rat-cubes,
member-rat-cube-faces,
istype-nat,
nat_plus_wf,
istype-le,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
nat_plus_properties,
rational-cube-complex_wf,
l_all_wf2,
pairwise_wf2,
no_repeats_wf,
less_than_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
rat-cube-dimension_wf,
equal-wf-base,
l_all_iff,
l_member_wf,
member-face-complex,
compatible-rat-cubes-refl,
compatible-rat-cubes-symm,
compatible-rat-cubes_wf,
Error :pairwise-iff,
remove-repeats-no_repeats,
rational-cube_wf,
nil_wf,
rat-cube-faces_wf,
eqtt_to_assert,
map_wf,
concat_wf,
rc-deq_wf,
remove-repeats_wf
Rules used in proof :
universeEquality,
sqequalBase,
productEquality,
setEquality,
imageElimination,
imageMemberEquality,
isectIsTypeImplies,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
axiomEquality,
productIsType,
setIsType,
baseClosed,
closedConclusion,
baseApply,
addEquality,
natural_numberEquality,
minusEquality,
rename,
setElimination,
intEquality,
cumulativity,
instantiate,
independent_pairFormation,
dependent_set_memberEquality_alt,
universeIsType,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
hypothesisEquality,
applyEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
lambdaFormation_alt,
inhabitedIsType,
lambdaEquality_alt,
hypothesis,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[K:n-dim-complex]. (face-complex(k;K) \mmember{} n - 1-dim-complex)
Date html generated:
2019_10_29-AM-07_57_55
Last ObjectModification:
2019_10_19-AM-02_14_30
Theory : rationals
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