Nuprl Lemma : subterm-varterm
∀[opr:Type]. ∀[s:term(opr)]. ∀[v:{v:varname()| ¬(v = nullvar() ∈ varname())} ]. (¬s << varterm(v))
Proof
Definitions occuring in Statement :
subterm: s << t,
varterm: varterm(v),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
uimplies: b supposing a,
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
subterm-size,
varterm_wf,
term_size_var_lemma,
term-size-positive,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
subterm_wf,
nullvar_wf,
varname_wf,
istype-void,
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,
because_Cache,
independent_isectElimination,
setElimination,
rename,
hypothesis,
independent_functionElimination,
voidElimination,
sqequalRule,
dependent_functionElimination,
Error :memTop,
productElimination,
natural_numberEquality,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
universeIsType,
equalityIstype,
inhabitedIsType,
functionIsTypeImplies,
setIsType,
functionIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s:term(opr)]. \mforall{}[v:\{v:varname()| \mneg{}(v = nullvar())\} ]. (\mneg{}s << varterm(v))
Date html generated:
2020_05_19-PM-09_54_15
Last ObjectModification:
2020_03_12-AM-11_08_49
Theory : terms
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