Nuprl Lemma : increasing-zero-seq
increasing-sequence(0s)
Proof
Definitions occuring in Statement : 
increasing-sequence: increasing-sequence(a)
, 
zero-seq: 0s
Definitions unfolded in proof : 
top: Top
, 
exists: ∃x:A. B[x]
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
uimplies: b supposing a
, 
decidable: Dec(P)
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
less_than': less_than'(a;b)
, 
and: P ∧ Q
, 
le: A ≤ B
, 
ge: i ≥ j 
, 
nat: ℕ
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
or: P ∨ Q
, 
all: ∀x:A. B[x]
, 
increasing-sequence: increasing-sequence(a)
, 
zero-seq: 0s
Lemmas referenced : 
nat_wf, 
equal-wf-base, 
int_formula_prop_wf, 
decidable__equal_int, 
int_term_value_constant_lemma, 
int_formula_prop_eq_lemma, 
int_formula_prop_not_lemma, 
itermConstant_wf, 
intformeq_wf, 
intformnot_wf, 
satisfiable-full-omega-tt, 
le_wf, 
false_wf, 
decidable__equal_nat, 
nat_properties
Rules used in proof : 
baseClosed, 
equalitySymmetry, 
equalityTransitivity, 
computeAll, 
independent_functionElimination, 
voidEquality, 
voidElimination, 
isect_memberEquality, 
intEquality, 
lambdaEquality, 
dependent_pairFormation, 
independent_isectElimination, 
unionElimination, 
because_Cache, 
independent_pairFormation, 
natural_numberEquality, 
dependent_set_memberEquality, 
dependent_functionElimination, 
rename, 
setElimination, 
hypothesis, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
inlFormation, 
lambdaFormation, 
sqequalRule, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
increasing-sequence(0s)
Date html generated:
2017_04_21-AM-11_23_11
Last ObjectModification:
2017_04_20-PM-04_50_05
Theory : continuity
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