Nuprl Lemma : super-fact_wf

[n:ℕ]. ((n)!! ∈ ℕ+)


Proof




Definitions occuring in Statement :  super-fact: (n)!! nat_plus: + nat: uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T super-fact: (n)!! nat_plus: + less_than: a < b squash: T less_than': less_than'(a;b) true: True and: P ∧ Q prop: nat: int_seg: {i..j-} guard: {T} ge: i ≥  lelt: i ≤ j < k all: x:A. B[x] decidable: Dec(P) or: P ∨ Q uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top
Lemmas referenced :  nat_wf int_seg_wf le_wf int_formula_prop_wf int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermAdd_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties int_seg_properties nat_plus_properties fact_wf mul_nat_plus less_than_wf nat_plus_wf primrec_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed lambdaEquality addEquality setElimination rename productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll because_Cache axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[n:\mBbbN{}].  ((n)!!  \mmember{}  \mBbbN{}\msupplus{})



Date html generated: 2018_05_21-PM-01_04_33
Last ObjectModification: 2018_01_28-PM-02_13_11

Theory : num_thy_1


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