Nuprl Lemma : vars-of-subst_wf
∀[opr:Type]. ∀[s:(varname() × term(opr)) List]. (vars-of-subst(s) ∈ {v:varname()| ¬(v = nullvar() ∈ varname())} List)
Proof
Definitions occuring in Statement :
vars-of-subst: vars-of-subst(s),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
set: {x:A| B[x]} ,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vars-of-subst: vars-of-subst(s),
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
l-union-list_wf,
varname_wf,
not_wf,
equal_wf,
nullvar_wf,
var-deq_wf,
map_wf,
term_wf,
list_wf,
eq_var_wf,
free-vars_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal-wf-T-base,
assert-eq_var,
insert_wf,
istype-void,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
setEquality,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
productEquality,
lambdaEquality_alt,
productElimination,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality_alt,
functionIsType,
productIsType,
universeIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s:(varname() \mtimes{} term(opr)) List].
(vars-of-subst(s) \mmember{} \{v:varname()| \mneg{}(v = nullvar())\} List)
Date html generated:
2020_05_19-PM-09_57_42
Last ObjectModification:
2020_03_09-PM-04_09_56
Theory : terms
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