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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