Nuprl Lemma : vr_test_foo_bar345566
ℕ7 ⋂ {3..9-} ≡ {3..7-}
Proof
Definitions occuring in Statement :
isect2: T1 ⋂ T2,
int_seg: {i..j-},
ext-eq: A ≡ B,
natural_number: $n
Definitions unfolded in proof :
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
int_seg: {i..j-},
uimplies: b supposing a,
or: P ∨ Q,
lelt: i ≤ j < k,
guard: {T},
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
le: A ≤ B
Lemmas referenced :
bool_wf,
int_formula_prop_less_lemma,
intformless_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,
satisfiable-full-omega-tt,
decidable__le,
lelt_wf,
int_seg_properties,
subtype_rel_wf,
isect2_subtype_rel3,
isect2_decomp,
int_seg_wf,
isect2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
applyEquality,
because_Cache,
intEquality,
independent_isectElimination,
inlFormation,
setElimination,
rename,
sqequalRule,
setEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityElimination
Latex:
\mBbbN{}7 \mcap{} \{3..9\msupminus{}\} \mequiv{} \{3..7\msupminus{}\}
Date html generated:
2016_05_15-PM-07_56_37
Last ObjectModification:
2016_01_16-AM-09_40_20
Theory : general
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