Nuprl Lemma : nil-sublist
∀[T,x:Top]. [] ⊆ x
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
nil: [],
uall: ∀[x:A]. B[x],
top: Top
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sublist: L1 ⊆ L2,
select: L[n],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
increasing: increasing(f;k),
subtract: n - m
Lemmas referenced :
length_of_nil_lemma,
stuck-spread,
istype-base,
istype-void,
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
increasing_wf,
false_wf,
le_wf,
equal-wf-base-T,
select_wf,
istype-top,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
Error :lambdaFormation_alt,
Error :isect_memberEquality_alt,
voidElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
natural_numberEquality,
because_Cache,
hypothesisEquality,
setElimination,
rename,
productElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
dependent_functionElimination,
independent_pairFormation,
Error :universeIsType,
Error :productIsType,
Error :dependent_set_memberEquality_alt,
functionExtensionality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
Error :functionIsType,
instantiate,
Error :inhabitedIsType
Latex:
\mforall{}[T,x:Top]. [] \msubseteq{} x
Date html generated:
2019_06_20-PM-01_22_28
Last ObjectModification:
2018_09_29-PM-00_28_18
Theory : list_1
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