Nuprl Lemma : int-rdiv_functionality
∀[k1,k2:ℤ-o]. ∀[a,b:ℝ]. ((a)/k1 = (b)/k2) supposing ((k1 = k2 ∈ ℤ) and (a = b))
Proof
Definitions occuring in Statement :
int-rdiv: (a)/k1,
req: x = y,
real: ℝ,
int_nzero: ℤ-o,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_nzero: ℤ-o,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
not: ¬A,
nequal: a ≠ b ∈ T ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
true: True,
squash: ↓T
Lemmas referenced :
req_functionality,
int-rdiv_wf,
rdiv_wf,
int-to-real_wf,
rneq-int,
int_nzero_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
equal-wf-T-base,
int-rdiv-req,
req_witness,
equal_wf,
req_wf,
real_wf,
int_nzero_wf,
req_weakening,
rdiv_functionality,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
productElimination,
independent_functionElimination,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
baseClosed,
applyEquality,
imageElimination,
imageMemberEquality
Latex:
\mforall{}[k1,k2:\mBbbZ{}\msupminus{}\msupzero{}]. \mforall{}[a,b:\mBbbR{}]. ((a)/k1 = (b)/k2) supposing ((k1 = k2) and (a = b))
Date html generated:
2016_10_26-AM-09_09_21
Last ObjectModification:
2016_08_26-PM-01_57_13
Theory : reals
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