Nuprl Lemma : vars-of-subst-not-nullvar
∀[opr:Type]. ∀[s:(varname() × term(opr)) List]. (¬(nullvar() ∈ vars-of-subst(s)))
Proof
Definitions occuring in Statement :
vars-of-subst: vars-of-subst(s),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
prop: ℙ,
nat: ℕ,
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
vars-of-subst_wf,
select_wf,
varname_wf,
not_wf,
equal_wf,
nullvar_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
l_member_wf,
subtype_rel_list,
equal-wf-T-base,
istype-void,
list_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
inhabitedIsType,
productElimination,
closedConclusion,
setEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
sqequalRule,
independent_pairFormation,
universeIsType,
voidElimination,
equalitySymmetry,
equalityIstype,
equalityTransitivity,
applyEquality,
baseClosed,
setIsType,
functionIsType,
functionIsTypeImplies,
productEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s:(varname() \mtimes{} term(opr)) List]. (\mneg{}(nullvar() \mmember{} vars-of-subst(s)))
Date html generated:
2020_05_19-PM-09_57_44
Last ObjectModification:
2020_03_09-PM-04_09_58
Theory : terms
Home
Index