Nuprl Lemma : append-impossible2
∀[T:Type]. ∀[as,bs,cs:T List]. ∀[b:T]. uiff(cs = (as @ [b / bs]) ∈ (T List);False) supposing cs ≤ as
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
append: as @ bs,
cons: [a / b],
list: T List,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
false: False,
prop: ℙ,
squash: ↓T,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A
Lemmas referenced :
iseg_length,
le_wf,
length_wf,
squash_wf,
true_wf,
length_append,
subtype_rel_list,
top_wf,
cons_wf,
iff_weakening_equal,
length_of_cons_lemma,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
equal_wf,
list_wf,
append_wf,
false_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_isectElimination,
hypothesis,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
computeAll,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs,cs:T List]. \mforall{}[b:T]. uiff(cs = (as @ [b / bs]);False) supposing cs \mleq{} as
Date html generated:
2016_10_25-AM-10_16_33
Last ObjectModification:
2016_07_12-AM-06_35_05
Theory : list!
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