Nuprl Lemma : context-lookup_wf
∀[Gamma:mFOL() List]. ∀[x:ℕ||Gamma||]. (context-lookup(Gamma;x) ∈ mFOL())
Proof
Definitions occuring in Statement :
context-lookup: context-lookup(Gamma;x),
mFOL: mFOL(),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
context-lookup: context-lookup(Gamma;x),
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
list_wf,
int_seg_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermAdd_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
length_wf,
subtract_wf,
mFOL_wf,
select_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
because_Cache,
addEquality,
setElimination,
rename,
natural_numberEquality,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[Gamma:mFOL() List]. \mforall{}[x:\mBbbN{}||Gamma||]. (context-lookup(Gamma;x) \mmember{} mFOL())
Date html generated:
2016_05_15-PM-10_31_42
Last ObjectModification:
2016_01_16-PM-04_31_48
Theory : minimal-first-order-logic
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