Nuprl Lemma : member_upto2
∀n,i:ℕ. (i ∈ upto(n)) supposing i < n
Proof
Definitions occuring in Statement :
upto: upto(n),
l_member: (x ∈ l),
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
prop: ℙ,
cand: A c∧ B,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top
Lemmas referenced :
member-less_than,
length_upto,
select_upto,
lelt_wf,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
less_than_wf,
length_wf,
int_seg_wf,
upto_wf,
equal_wf,
select_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_pairFormation,
sqequalRule,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
productElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
natural_numberEquality,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
productEquality
Latex:
\mforall{}n,i:\mBbbN{}. (i \mmember{} upto(n)) supposing i < n
Date html generated:
2017_04_17-AM-07_58_09
Last ObjectModification:
2017_02_27-PM-04_29_19
Theory : list_1
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