Nuprl Lemma : frs-refines_weakening
∀[p,q:ℝ List]. ((p = q ∈ (ℝ List)) ⇒ frs-refines(p;q))
Proof
Definitions occuring in Statement :
frs-refines: frs-refines(p;q),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
frs-refines: frs-refines(p;q),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
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,
less_than: a < b,
squash: ↓T
Lemmas referenced :
length_wf_nat,
real_wf,
equal_wf,
nat_wf,
req_weakening,
select_wf,
int_seg_properties,
length_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
req_wf,
int_seg_wf,
frs-refines_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
dependent_set_memberEquality,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_pairFormation,
because_Cache,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
imageElimination,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality
Latex:
\mforall{}[p,q:\mBbbR{} List]. ((p = q) {}\mRightarrow{} frs-refines(p;q))
Date html generated:
2016_10_26-AM-09_32_25
Last ObjectModification:
2016_07_12-AM-08_19_47
Theory : reals
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