Nuprl Lemma : upto_iseg
∀i,j:ℕ. upto(i) ≤ upto(j) supposing i ≤ j
Proof
Definitions occuring in Statement :
upto: upto(n),
iseg: l1 ≤ l2,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
iseg: l1 ≤ l2,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B
Lemmas referenced :
nat_wf,
le_wf,
list_wf,
equal_wf,
int_seg_subtype,
subtype_rel_list,
append_wf,
upto_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
decidable__le,
add-member-int_seg2,
subtract_wf,
int_seg_wf,
map_wf,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
upto_decomp,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
addEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll,
because_Cache,
applyEquality
Latex:
\mforall{}i,j:\mBbbN{}. upto(i) \mleq{} upto(j) supposing i \mleq{} j
Date html generated:
2016_05_14-PM-02_04_12
Last ObjectModification:
2016_01_15-AM-08_05_22
Theory : list_1
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