Nuprl Lemma : tree_subtype

[A,B:Type].  tree(A) ⊆tree(B) supposing A ⊆B


Proof




Definitions occuring in Statement :  tree: tree(E) uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a subtype_rel: A ⊆B all: x:A. B[x] nat: implies:  Q false: False ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A top: Top and: P ∧ Q prop: guard: {T} int_seg: {i..j-} lelt: i ≤ j < k decidable: Dec(P) or: P ∨ Q le: A ≤ B less_than': less_than'(a;b) ext-eq: A ≡ B bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) sq_type: SQType(T) eq_atom: =a y ifthenelse: if then else fi  tree_leaf: tree_leaf(value) tree_size: tree_size(p) bfalse: ff bnot: ¬bb assert: b tree_node: tree_node(left;right) cand: c∧ B less_than: a < b squash: T
Lemmas referenced :  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 le_wf tree_size_wf int_seg_wf int_seg_properties decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma decidable__equal_int int_seg_subtype false_wf intformeq_wf int_formula_prop_eq_lemma tree-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base tree_leaf_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom decidable__lt itermAdd_wf int_term_value_add_lemma lelt_wf nat_wf tree_node_wf tree_wf subtype_rel_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry cumulativity applyEquality because_Cache productElimination unionElimination applyLambdaEquality hypothesis_subsumption dependent_set_memberEquality promote_hyp tokenEquality equalityElimination instantiate atomEquality imageElimination addEquality universeEquality

Latex:
\mforall{}[A,B:Type].    tree(A)  \msubseteq{}r  tree(B)  supposing  A  \msubseteq{}r  B



Date html generated: 2017_10_01-AM-08_30_38
Last ObjectModification: 2017_07_26-PM-04_24_41

Theory : tree_1


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