Nuprl Lemma : rtermDivide_wf
∀[num,denom:rat_term()]. (num "/" denom ∈ rat_term())
Proof
Definitions occuring in Statement :
rtermDivide: num "/" denom,
rat_term: rat_term(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rat_term: rat_term(),
rtermDivide: num "/" denom,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
rat_termco_size: rat_termco_size(p),
rat_term_size: rat_term_size(p),
pi1: fst(t),
pi2: snd(t),
nat: 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,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rat_termco-ext,
ifthenelse_wf,
eq_atom_wf,
rat_termco_wf,
add_nat_wf,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
rat_term_size_wf,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
istype-universe,
has-value_wf-partial,
rat_termco_size_wf,
rat_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
dependent_set_memberEquality_alt,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality_alt,
tokenEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
inhabitedIsType,
universeIsType,
instantiate,
isectElimination,
universeEquality,
intEquality,
productEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[num,denom:rat\_term()]. (num "/" denom \mmember{} rat\_term())
Date html generated:
2019_10_29-AM-09_26_46
Last ObjectModification:
2019_03_31-PM-05_24_20
Theory : reals
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