Nuprl Lemma : mFOL-evidence-value-type
∀[fmla:mFOL()]. value-type(mFOL-evidence(fmla))
Proof
Definitions occuring in Statement :
mFOL-evidence: mFOL-evidence(fmla),
mFOL: mFOL(),
value-type: value-type(T),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOL-evidence: mFOL-evidence(fmla),
mFO-uniform-evidence: mFO-uniform-evidence(vs;fmla),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
FOStruct: FOStruct(Dom),
uimplies: b supposing a,
top: Top,
FOAssignment: FOAssignment(vs,Dom),
FOSatWith: Dom,S,a |= fmla,
squash: ↓T,
value-type: value-type(T),
has-value: (a)↓,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
mFOatomic: name(vars),
mFOL_size: mFOL_size(p),
spreadn: spread3,
mFOL-abstract: mFOL-abstract(fmla),
mFOL_ind: mFOL_ind,
AbstractFOAtomic: AbstractFOAtomic(n;L),
true: True,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
mFOconnect: mFOconnect(knd;left;right),
cand: A c∧ B,
less_than: a < b,
FOConnective: FOConnective(knd),
let: let,
mFOquant: mFOquant(isall;var;body),
FOQuantifier: FOQuantifier(isall),
AbstractFOFormula: AbstractFOFormula(vs),
update-assignment: a[x := v]
Lemmas referenced :
isect-value-type,
FOStruct_wf,
all_wf,
FOAssignment_wf,
mFOL-freevars_wf,
FOSatWith_wf,
mFOL-abstract_wf,
unit_wf2,
true_wf,
top_wf,
subtype_rel_dep_function,
list_wf,
subtype_rel_self,
function-value-type,
it_wf,
l_member_wf,
set_wf,
value-type_wf,
equal-wf-base,
mFOL-evidence_wf,
base_wf,
mFOL_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
le_wf,
mFOL_size_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
mFOL-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
equal-value-type,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
lelt_wf,
product-value-type,
union-value-type,
update-assignment_wf,
nat_wf,
AbstractFOFormula_wf,
subtype_rel-equal,
filter_wf5,
bnot_wf,
eq_int_wf,
equal-unit,
ifthenelse_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
sqequalRule,
lambdaEquality,
isectEquality,
cumulativity,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_pairFormation,
applyEquality,
functionEquality,
atomEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
because_Cache,
setEquality,
intEquality,
imageMemberEquality,
baseClosed,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
int_eqEquality,
dependent_functionElimination,
independent_pairFormation,
computeAll,
productElimination,
unionElimination,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
promote_hyp,
tokenEquality,
equalityElimination,
imageElimination,
addEquality,
axiomEquality,
independent_pairEquality,
productEquality,
inlEquality,
functionExtensionality,
dependent_pairEquality,
hyp_replacement
Latex:
\mforall{}[fmla:mFOL()]. value-type(mFOL-evidence(fmla))
Date html generated:
2018_05_21-PM-10_24_52
Last ObjectModification:
2017_07_26-PM-06_38_41
Theory : minimal-first-order-logic
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