Nuprl Lemma : frs-mesh_wf
∀[p:ℝ List]. (frs-mesh(p) ∈ ℝ)
Proof
Definitions occuring in Statement :
frs-mesh: frs-mesh(p),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
frs-mesh: frs-mesh(p),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
so_apply: x[s]
Lemmas referenced :
lt_int_wf,
length_wf,
real_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
int-to-real_wf,
le_int_wf,
le_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
rmaximum_wf,
subtract_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_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_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
rsub_wf,
select_wf,
int_seg_properties,
itermAdd_wf,
int_term_value_add_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
addEquality,
setElimination,
rename,
axiomEquality
Latex:
\mforall{}[p:\mBbbR{} List]. (frs-mesh(p) \mmember{} \mBbbR{})
Date html generated:
2017_10_03-AM-09_35_54
Last ObjectModification:
2017_07_28-AM-07_53_40
Theory : reals
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