Nuprl Lemma : interval-vec-subtype
∀[I:Interval]. ∀[n,m:ℕ]. I^m ⊆r I^n supposing n ≤ m
Proof
Definitions occuring in Statement :
interval-vec: I^n,
interval: Interval,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
real-vec: ℝ^n,
nat: ℕ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
interval-vec: I^n
Lemmas referenced :
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__lt,
nat_properties,
interval_wf,
nat_wf,
le_wf,
real-vec-subtype,
subtype_rel_set,
i-member_wf,
int_seg_wf,
all_wf,
real-vec_wf,
subtype_rel_sets
Rules used in proof :
voidEquality,
voidElimination,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
productElimination,
dependent_set_memberEquality,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
axiomEquality,
lambdaFormation,
independent_isectElimination,
because_Cache,
applyEquality,
rename,
setElimination,
natural_numberEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. \mforall{}[n,m:\mBbbN{}]. I\^{}m \msubseteq{}r I\^{}n supposing n \mleq{} m
Date html generated:
2018_07_29-AM-09_45_05
Last ObjectModification:
2018_07_02-PM-01_17_36
Theory : reals
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