Nuprl Lemma : rat-midpoint_wf
∀[a,b:ℤ × ℕ+]. (rat-midpoint(a;b) ∈ ℤ × ℕ+)
Proof
Definitions occuring in Statement :
rat-midpoint: rat-midpoint(a;b),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rat-midpoint: rat-midpoint(a;b),
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False
Lemmas referenced :
rat-nat-div_wf,
ratadd_wf,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
isect_memberEquality_alt,
voidElimination,
universeIsType,
axiomEquality,
isectIsTypeImplies,
productIsType
Latex:
\mforall{}[a,b:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. (rat-midpoint(a;b) \mmember{} \mBbbZ{} \mtimes{} \mBbbN{}\msupplus{})
Date html generated:
2019_10_30-AM-09_31_44
Last ObjectModification:
2019_02_17-PM-06_13_19
Theory : reals
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