Nuprl Lemma : weak-Markov-principle2-alt
∀a:ℕ*. ((∀c:ℕ*. ((¬(a = c ∈ ℕ*)) ∨ (¬(0 = c ∈ ℕ*)))) ⇒ (∃n:ℕ. 0 < a n))
Proof
Definitions occuring in Statement :
nat-star-0: 0,
nat-star: ℕ*,
nat: ℕ,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
apply: f a,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
nat-star-0: 0,
guard: {T},
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
nat: ℕ,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
decidable: Dec(P),
nat-star: ℕ*,
not: ¬A,
or: P ∨ Q,
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
int_formula_prop_le_lemma,
intformle_wf,
decidable__le,
int_term_value_constant_lemma,
itermConstant_wf,
or_wf,
nat-star_wf,
nat-star-0_wf,
equal-wf-base-T,
exists_wf,
less_than_wf,
all_wf,
not_wf,
equal_wf,
int_formula_prop_wf,
le_wf,
zero-le-nat,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
nat_wf,
decidable__equal_nat,
weak-Markov-principle2
Rules used in proof :
inrFormation,
baseClosed,
functionEquality,
because_Cache,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
equalityTransitivity,
isectElimination,
dependent_pairFormation,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
rename,
setElimination,
equalitySymmetry,
inlFormation,
unionElimination,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}a:\mBbbN{}*. ((\mforall{}c:\mBbbN{}*. ((\mneg{}(a = c)) \mvee{} (\mneg{}(0 = c)))) {}\mRightarrow{} (\mexists{}n:\mBbbN{}. 0 < a n))
Date html generated:
2017_09_29-PM-06_06_48
Last ObjectModification:
2017_09_05-PM-02_39_55
Theory : continuity
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