Nuprl Lemma : context-lookup-stable1
∀[Gamma,more:mFOL() List]. ∀[x:ℕ||Gamma||]. (context-lookup(more @ Gamma;x) ~ context-lookup(Gamma;x))
Proof
Definitions occuring in Statement :
context-lookup: context-lookup(Gamma;x),
mFOL: mFOL(),
length: ||as||,
append: as @ bs,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
context-lookup: context-lookup(Gamma;x),
top: Top,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
int_seg: {i..j-},
ge: i ≥ j ,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
less_than: a < b,
squash: ↓T,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
length-append,
select-append,
subtype_rel_list,
mFOL_wf,
top_wf,
subtract_wf,
length_wf,
non_neg_length,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
intformless_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_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
int_seg_wf,
list_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
int_subtype_base,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
sqequalAxiom,
lambdaFormation,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
imageElimination,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination
Latex:
\mforall{}[Gamma,more:mFOL() List]. \mforall{}[x:\mBbbN{}||Gamma||].
(context-lookup(more @ Gamma;x) \msim{} context-lookup(Gamma;x))
Date html generated:
2018_05_21-PM-10_41_02
Last ObjectModification:
2017_07_26-PM-06_42_28
Theory : minimal-first-order-logic
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