Nuprl Lemma : rat-interval-dimension_wf
∀[I:ℚInterval]. (dim(I) ∈ ℕ2)
Proof
Definitions occuring in Statement :
rat-interval-dimension: dim(I),
rational-interval: ℚInterval,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
false: False,
prop: ℙ,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
rational-interval: ℚInterval,
rat-interval-dimension: dim(I),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rational-interval_wf,
istype-less_than,
istype-le,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
istype-void,
int_formula_prop_not_lemma,
istype-int,
itermConstant_wf,
intformle_wf,
intformnot_wf,
full-omega-unsat,
decidable__le,
int_seg_wf,
q_le_wf,
ifthenelse_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productIsType,
universeIsType,
voidElimination,
isect_memberEquality_alt,
lambdaEquality_alt,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
dependent_set_memberEquality_alt,
natural_numberEquality,
hypothesis,
isectElimination,
extract_by_obid,
hypothesisEquality,
independent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
spreadEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:\mBbbQ{}Interval]. (dim(I) \mmember{} \mBbbN{}2)
Date html generated:
2019_10_29-AM-07_47_55
Last ObjectModification:
2019_10_17-PM-01_55_25
Theory : rationals
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