Nuprl Lemma : single-valued-bag-if-le1

`∀[T:Type]. ∀[b:bag(T)].  single-valued-bag(b;T) supposing #(b) ≤ 1`

Proof

Definitions occuring in Statement :  single-valued-bag: `single-valued-bag(b;T)` bag-size: `#(bs)` bag: `bag(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` single-valued-bag: `single-valued-bag(b;T)` all: `∀x:A. B[x]` implies: `P `` Q` subtype_rel: `A ⊆r B` decidable: `Dec(P)` or: `P ∨ Q` nat: `ℕ` guard: `{T}` so_lambda: `λ2x.t[x]` prop: `ℙ` so_apply: `x[s]` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` and: `P ∧ Q` squash: `↓T` bag-size: `#(bs)` uiff: `uiff(P;Q)` empty-bag: `{}` true: `True` iff: `P `⇐⇒` Q` single-bag: `{x}`
Lemmas referenced :  decidable__or equal-wf-T-base bag-size_wf decidable__equal_int nat_properties set_wf le_wf satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformnot_wf intformor_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_formula_prop_or_lemma int_formula_prop_eq_lemma int_formula_prop_wf bag_to_squash_list or_wf bag-member_wf nat_wf bag_wf length_zero length_wf_nat equal_wf subtype_rel_set list_wf list-subtype-bag bag-member-empty-iff length_one squash_wf true_wf iff_weakening_equal bag-member-single
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination thin intEquality cumulativity hypothesisEquality hypothesis applyEquality because_Cache sqequalRule baseClosed independent_functionElimination dependent_functionElimination natural_numberEquality unionElimination equalityTransitivity equalitySymmetry lambdaEquality setElimination rename independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination productElimination promote_hyp hyp_replacement Error :applyLambdaEquality,  axiomEquality universeEquality dependent_set_memberEquality imageMemberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[b:bag(T)].    single-valued-bag(b;T)  supposing  \#(b)  \mleq{}  1

Date html generated: 2016_10_25-AM-10_29_23
Last ObjectModification: 2016_07_12-AM-06_45_36

Theory : bags

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