### Nuprl Lemma : bool-cardinality-le

`|𝔹| ≤ 2`

Proof

Definitions occuring in Statement :  cardinality-le: `|T| ≤ n` bool: `𝔹` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` implies: `P `` Q` length: `||as||` list_ind: list_ind cons: `[a / b]` nil: `[]` it: `⋅` bool: `𝔹` unit: `Unit` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` l_member: `(x ∈ l)` exists: `∃x:A. B[x]` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` not: `¬A` false: `False` select: `L[n]` cand: `A c∧ B` less_than: `a < b` squash: `↓T` true: `True` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` prop: `ℙ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` subtract: `n - m`
Lemmas referenced :  list-cardinality-le bool_wf cons_wf btrue_wf bfalse_wf nil_wf eqtt_to_assert istype-void istype-le length_of_cons_lemma length_of_nil_lemma istype-less_than length_wf select_wf nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf istype-int 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 eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesis dependent_functionElimination independent_functionElimination sqequalRule lambdaFormation_alt hypothesisEquality inhabitedIsType unionElimination equalityElimination productElimination independent_isectElimination dependent_pairFormation_alt dependent_set_memberEquality_alt natural_numberEquality independent_pairFormation voidElimination Error :memTop,  imageMemberEquality baseClosed productIsType setElimination rename equalityIstype because_Cache approximateComputation lambdaEquality_alt int_eqEquality universeIsType sqequalBase equalitySymmetry equalityTransitivity promote_hyp instantiate cumulativity

Latex:
|\mBbbB{}|  \mleq{}  2

Date html generated: 2020_05_19-PM-09_43_31
Last ObjectModification: 2019_12_31-PM-00_28_25

Theory : list_1

Home Index