### Nuprl Lemma : length_sublist

`∀[T:Type]. ∀[L1,L2:T List].  ||L1|| ≤ ||L2|| supposing L1 ⊆ L2`

Proof

Definitions occuring in Statement :  sublist: `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 :  sublist: `L1 ⊆ L2` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` exists: `∃x:A. B[x]` and: `P ∧ Q` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` prop: `ℙ` subtype_rel: `A ⊆r B` int_seg: `{i..j-}` all: `∀x:A. B[x]` guard: `{T}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` less_than: `a < b` squash: `↓T` ge: `i ≥ j ` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  less_than'_wf length_wf int_seg_wf increasing_wf length_wf_nat equal_wf select_wf int_seg_properties 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 decidable__lt intformless_wf int_formula_prop_less_lemma non_neg_length lelt_wf nat_properties exists_wf all_wf list_wf increasing_le
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  introduction cut sqequalHypSubstitution productElimination thin independent_pairEquality lambdaEquality dependent_functionElimination hypothesisEquality because_Cache extract_by_obid isectElimination hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :productIsType,  Error :functionIsType,  Error :universeIsType,  natural_numberEquality functionExtensionality applyEquality setElimination rename cumulativity independent_isectElimination unionElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation imageElimination dependent_set_memberEquality applyLambdaEquality functionEquality productEquality Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L1,L2:T  List].    ||L1||  \mleq{}  ||L2||  supposing  L1  \msubseteq{}  L2

Date html generated: 2019_06_20-PM-01_22_19
Last ObjectModification: 2018_09_26-PM-05_20_50

Theory : list_1

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