Nuprl Lemma : row-list-matrix_wf
∀[n,m:ℕ]. ∀[r:RngSig]. ∀[L:|r| List List].
(row-list-matrix(L) ∈ Matrix(n;m;r)) supposing ((∀i:ℕn. (m ≤ ||L[i]||)) and (n ≤ ||L||))
Proof
Definitions occuring in Statement :
row-list-matrix: row-list-matrix(L),
matrix: Matrix(n;m;r),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
member: t ∈ T,
natural_number: $n,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
le: A ≤ B,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
and: P ∧ Q,
lelt: i ≤ j < k,
guard: {T},
int_seg: {i..j-},
so_lambda: λ2x y.t[x; y],
nat: ℕ,
row-list-matrix: row-list-matrix(L),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
rng_sig_wf,
le_wf,
all_wf,
int_seg_wf,
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,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
list_wf,
rng_car_wf,
select_wf,
mx_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
unionElimination,
dependent_functionElimination,
productElimination,
natural_numberEquality,
independent_isectElimination,
lambdaEquality,
hypothesisEquality,
hypothesis,
rename,
setElimination,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[r:RngSig]. \mforall{}[L:|r| List List].
(row-list-matrix(L) \mmember{} Matrix(n;m;r)) supposing ((\mforall{}i:\mBbbN{}n. (m \mleq{} ||L[i]||)) and (n \mleq{} ||L||))
Date html generated:
2018_05_21-PM-09_45_07
Last ObjectModification:
2017_12_14-PM-05_34_49
Theory : matrices
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