Nuprl Lemma : free-from-atom-rational
∀[a:Atom1]. ∀[q:ℚ].  a#q:ℚ
Proof
Definitions occuring in Statement : 
rationals: ℚ
, 
free-from-atom: a#x:T
, 
atom: Atom$n
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
nat_plus: ℕ+
, 
cand: A c∧ B
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
int_nzero: ℤ-o
, 
nequal: a ≠ b ∈ T 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
false: False
, 
top: Top
, 
prop: ℙ
, 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
guard: {T}
Lemmas referenced : 
q-elim, 
nat_plus_properties, 
iff_weakening_uiff, 
assert_wf, 
qeq_wf2, 
int-subtype-rationals, 
equal-wf-base, 
rationals_wf, 
int_subtype_base, 
assert-qeq, 
istype-assert, 
full-omega-unsat, 
intformand_wf, 
intformeq_wf, 
itermVar_wf, 
itermConstant_wf, 
intformless_wf, 
istype-int, 
int_formula_prop_and_lemma, 
istype-void, 
int_formula_prop_eq_lemma, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
nequal_wf, 
free-from-atom_wf, 
free-from-atom-int, 
int_nzero_wf, 
int_nzero-rational, 
subtype_rel_set, 
qdiv_wf, 
subtype_rel_self
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
productElimination, 
isectElimination, 
hypothesis, 
setElimination, 
rename, 
lambdaFormation_alt, 
independent_functionElimination, 
applyEquality, 
sqequalRule, 
natural_numberEquality, 
because_Cache, 
baseClosed, 
dependent_set_memberEquality_alt, 
independent_isectElimination, 
approximateComputation, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
isect_memberEquality_alt, 
voidElimination, 
independent_pairFormation, 
universeIsType, 
equalityIstype, 
inhabitedIsType, 
sqequalBase, 
equalitySymmetry, 
intEquality, 
freeFromAtomApplication, 
hyp_replacement, 
applyLambdaEquality, 
cumulativity, 
freeFromAtomAxiom, 
isectIsTypeImplies, 
atomnEquality, 
lambdaEquality, 
freeFromAtomTriviality, 
setEquality, 
equalityTransitivity, 
freeFromAtomSet
Latex:
\mforall{}[a:Atom1].  \mforall{}[q:\mBbbQ{}].    a\#q:\mBbbQ{}
Date html generated:
2020_05_20-AM-09_31_16
Last ObjectModification:
2019_11_27-PM-02_15_14
Theory : randomness
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