Nuprl Lemma : mFOL-boundvars-of-rename
∀[fmla:mFOL()]. ∀[old,new:ℤ]. (mFOL-boundvars(mFOL-rename(fmla;old;new)) = mFOL-boundvars(fmla) ∈ (ℤ List))
Proof
Definitions occuring in Statement :
mFOL-rename: mFOL-rename(fmla;old;new),
mFOL-boundvars: mFOL-boundvars(fmla),
mFOL: mFOL(),
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
mFOL-boundvars: mFOL-boundvars(fmla),
mFOL_ind: mFOL_ind,
mFOL-rename: mFOL-rename(fmla;old;new),
mFOatomic: name(vars),
nil: [],
it: ⋅,
mFOconnect: mFOconnect(knd;left;right),
prop: ℙ,
mFOquant: mFOquant(isall;var;body),
guard: {T},
squash: ↓T,
true: True,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mFOL-induction,
equal_wf,
list_wf,
mFOL-boundvars_wf,
mFOL-rename_wf,
mFOL_wf,
mFOatomic_wf,
bool_wf,
l-union_wf,
squash_wf,
true_wf,
deq_wf,
int-deq_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
insert_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
intEquality,
hypothesis,
hypothesisEquality,
independent_functionElimination,
lambdaFormation,
atomEquality,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
equalityUniverse,
levelHypothesis
Latex:
\mforall{}[fmla:mFOL()]. \mforall{}[old,new:\mBbbZ{}]. (mFOL-boundvars(mFOL-rename(fmla;old;new)) = mFOL-boundvars(fmla))
Date html generated:
2018_05_21-PM-10_22_04
Last ObjectModification:
2017_07_26-PM-06_38_07
Theory : minimal-first-order-logic
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