Nuprl Lemma : fseg_length
∀[T:Type]. ∀[l1,l2:T List]. ||l1|| ≤ ||l2|| supposing fseg(T;l1;l2)
Proof
Definitions occuring in Statement :
fseg: fseg(T;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 :
fseg: fseg(T;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,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
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,
iff_weakening_equal,
non_neg_length,
decidable__le,
satisfiable-full-omega-tt,
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,
exists_wf,
list_wf,
equal_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
cumulativity,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
hyp_replacement,
Error :applyLambdaEquality,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. ||l1|| \mleq{} ||l2|| supposing fseg(T;l1;l2)
Date html generated:
2016_10_25-AM-10_45_22
Last ObjectModification:
2016_07_12-AM-06_55_27
Theory : general
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