Nuprl Lemma : frs-refines_transitivity
∀[p,q,r:ℝ List]. (frs-refines(p;q) ⇒ frs-refines(q;r) ⇒ frs-refines(p;r))
Proof
Definitions occuring in Statement :
frs-refines: frs-refines(p;q),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
frs-refines: frs-refines(p;q),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
member: t ∈ T,
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T
Lemmas referenced :
list_wf,
frs-refines_wf,
int_seg_wf,
req_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
length_wf,
int_seg_properties,
real_wf,
select_wf,
req_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
rename,
dependent_pairFormation,
cut,
hypothesis,
lemma_by_obid,
isectElimination,
setElimination,
independent_isectElimination,
natural_numberEquality,
unionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
because_Cache,
imageElimination
Latex:
\mforall{}[p,q,r:\mBbbR{} List]. (frs-refines(p;q) {}\mRightarrow{} frs-refines(q;r) {}\mRightarrow{} frs-refines(p;r))
Date html generated:
2016_05_18-AM-08_52_39
Last ObjectModification:
2016_01_17-AM-02_26_54
Theory : reals
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