### Nuprl Lemma : strong-subtype-bag

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

Proof

Definitions occuring in Statement :  bag: `bag(T)` 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` 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` implies: `P `` Q` all: `∀x:A. B[x]` bag-member: `x ↓∈ bs` squash: `↓T` and: `P ∧ Q` sq_stable: `SqStable(P)` bag: `bag(T)` quotient: `x,y:A//B[x; y]` guard: `{T}` iff: `P `⇐⇒` Q` l_member: `(x ∈ l)` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top`
Lemmas referenced :  subtype_rel_bag bag_wf exists_wf equal_wf strong-subtype_witness strong-subtype_wf bag-subtype bag-member_wf bag_to_squash_list sq_stable__all l_member_wf list-subtype-bag squash_wf sq_stable__squash member-permutation member_wf list_wf subtype_rel_list permutation_wf select_wf nat_properties decidable__le satisfiable-full-omega-tt 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 strong-subtype-implies
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis productElimination independent_pairFormation lambdaEquality setEquality cumulativity sqequalRule applyEquality because_Cache independent_functionElimination isect_memberEquality equalityTransitivity equalitySymmetry universeEquality dependent_functionElimination setElimination rename imageElimination functionEquality lambdaFormation imageMemberEquality baseClosed promote_hyp hyp_replacement applyLambdaEquality pertypeElimination productEquality dependent_pairFormation natural_numberEquality unionElimination int_eqEquality intEquality voidElimination voidEquality computeAll

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

Date html generated: 2017_10_01-AM-08_56_47
Last ObjectModification: 2017_07_26-PM-04_39_03

Theory : bags

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