Nuprl Lemma : pseudo-positive-almost-positive
∀[x:ℝ]. almost-positive(x) supposing pseudo-positive(x)
Proof
Definitions occuring in Statement :
pseudo-positive: pseudo-positive(x),
almost-positive: almost-positive(x),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
almost-positive: almost-positive(x),
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
false: False,
pseudo-positive: pseudo-positive(x),
all: ∀x:A. B[x],
or: P ∨ Q,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
not_wf,
rless_wf,
int-to-real_wf,
pseudo-positive_wf,
real_wf,
nat_plus_properties,
satisfiable-full-omega-tt,
intformless_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
voidElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
independent_functionElimination,
setElimination,
rename,
imageElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidEquality,
computeAll
Latex:
\mforall{}[x:\mBbbR{}]. almost-positive(x) supposing pseudo-positive(x)
Date html generated:
2017_01_09-AM-08_56_42
Last ObjectModification:
2016_11_16-PM-06_32_02
Theory : reals
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