### Nuprl Lemma : strong-subtype-list

`∀[A,B:Type].  strong-subtype(A List;B List) supposing strong-subtype(A;B)`

Proof

Definitions occuring in Statement :  list: `T List` strong-subtype: `strong-subtype(A;B)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` implies: `P `` Q` guard: `{T}` strong-subtype: `strong-subtype(A;B)` cand: `A c∧ B` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` exists: `∃x:A. B[x]` prop: `ℙ` all: `∀x:A. B[x]` nat: `ℕ` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` top: `Top` and: `P ∧ Q` or: `P ∨ Q` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` nil: `[]` it: `⋅` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)`
Lemmas referenced :  strong-subtype-implies subtype_rel_list list_wf exists_wf equal_wf strong-subtype_witness strong-subtype_wf nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases nil_wf equal-wf-base-T product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int null_nil_lemma btrue_wf null_cons_lemma bfalse_wf and_wf null_wf btrue_neq_bfalse subtype_rel_transitivity cons_wf reduce_hd_cons_lemma hd_wf squash_wf length_wf length_cons_ge_one top_wf reduce_tl_cons_lemma tl_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_functionElimination hypothesis productElimination independent_isectElimination independent_pairFormation lambdaEquality setEquality cumulativity sqequalRule applyEquality because_Cache isect_memberEquality equalityTransitivity equalitySymmetry universeEquality setElimination rename lambdaFormation intWeakElimination natural_numberEquality dependent_pairFormation int_eqEquality intEquality dependent_functionElimination voidElimination voidEquality computeAll axiomEquality unionElimination baseClosed promote_hyp hypothesis_subsumption applyLambdaEquality dependent_set_memberEquality addEquality instantiate imageElimination addLevel levelHypothesis imageMemberEquality

Latex:
\mforall{}[A,B:Type].    strong-subtype(A  List;B  List)  supposing  strong-subtype(A;B)

Date html generated: 2017_04_14-AM-09_27_20
Last ObjectModification: 2017_02_27-PM-04_01_16

Theory : list_1

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