Nuprl Lemma : whole_segment_example
∀T:Type. ∀as:T List. ((as[0..||as||-]) = as ∈ (T List))
Proof
Definitions occuring in Statement :
segment: as[m..n-],
length: ||as||,
list: T List,
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
int_iseg: {i...j},
and: P ∧ Q,
cand: A c∧ B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
list_wf,
segment_factor,
false_wf,
non_neg_length,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
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,
le_wf,
length_wf,
subtype_rel_self,
iff_weakening_equal,
lapp_fact_b
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
unionElimination,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productEquality,
imageMemberEquality,
baseClosed,
instantiate
Latex:
\mforall{}T:Type. \mforall{}as:T List. ((as[0..||as||\msupminus{}]) = as)
Date html generated:
2018_05_22-AM-07_45_37
Last ObjectModification:
2018_05_19-AM-08_32_51
Theory : list_2
Home
Index