Nuprl Lemma : not_permr_cons_nil
∀T:Type. ∀a:T. ∀as:T List. (¬([a / as] ≡(T) []))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
permr: as ≡(T) bs,
cand: A c∧ B,
top: Top,
ge: i ≥ j ,
exists: ∃x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Lemmas referenced :
permr_wf,
cons_wf,
nil_wf,
list_wf,
istype-universe,
length_of_cons_lemma,
istype-void,
length_of_nil_lemma,
non_neg_length,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_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_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf
Rules used in proof :
universeIsType,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
universeEquality,
lambdaFormation_alt,
independent_functionElimination,
voidElimination,
productElimination,
sqequalRule,
isect_memberEquality_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
independent_pairFormation
Latex:
\mforall{}T:Type. \mforall{}a:T. \mforall{}as:T List. (\mneg{}([a / as] \mequiv{}(T) []))
Date html generated:
2019_10_16-PM-01_00_22
Last ObjectModification:
2018_10_08-AM-10_29_25
Theory : perms_2
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