Nuprl Lemma : iseg_length
∀[T:Type]. ∀[l1,l2:T List]. ||l1|| ≤ ||l2|| supposing l1 ≤ l2
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
le_wf,
squash_wf,
true_wf,
length_wf,
length_append,
subtype_rel_list,
top_wf,
subtype_rel_self,
iff_weakening_equal,
non_neg_length,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
less_than'_wf,
equal_wf,
list_wf,
append_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
hyp_replacement,
applyLambdaEquality,
independent_pairEquality,
axiomEquality,
Error :productIsType,
Error :inhabitedIsType,
Error :universeIsType
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. ||l1|| \mleq{} ||l2|| supposing l1 \mleq{} l2
Date html generated:
2019_06_20-PM-01_29_49
Last ObjectModification:
2018_09_26-PM-05_59_30
Theory : list_1
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