Nuprl Lemma : fadd_increasing

[n:ℕ]. ∀[f,g:ℕn ⟶ ℤ].  (increasing(fadd(f;g);n)) supposing (nondecreasing(g;n) and increasing(f;n))


Definitions occuring in Statement :  fadd: fadd(f;g) nondecreasing: nondecreasing(f;k) increasing: increasing(f;k) int_seg: {i..j-} nat: uimplies: supposing a uall: [x:A]. B[x] function: x:A ⟶ B[x] natural_number: $n int:
Definitions unfolded in proof :  fadd: fadd(f;g) increasing: increasing(f;k) nondecreasing: nondecreasing(f;k) uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] guard: {T} nat: int_seg: {i..j-} ge: i ≥  lelt: i ≤ j < k and: P ∧ Q decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top prop: le: A ≤ B less_than: a < b squash: T uiff: uiff(P;Q) subtract: m so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  nat_wf less_than_wf le_wf all_wf add-member-int_seg2 member-less_than int_seg_wf int_term_value_add_lemma int_formula_prop_le_lemma itermAdd_wf intformle_wf decidable__le lelt_wf int_formula_prop_wf int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt nat_properties subtract_wf int_seg_properties
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality because_Cache lemma_by_obid isectElimination natural_numberEquality setElimination rename productElimination addEquality applyEquality dependent_set_memberEquality independent_pairFormation unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll imageElimination equalityTransitivity equalitySymmetry functionEquality

\mforall{}[n:\mBbbN{}].  \mforall{}[f,g:\mBbbN{}n  {}\mrightarrow{}  \mBbbZ{}].
    (increasing(fadd(f;g);n))  supposing  (nondecreasing(g;n)  and  increasing(f;n))

Date html generated: 2016_05_14-PM-09_30_07
Last ObjectModification: 2016_01_14-PM-11_33_33

Theory : num_thy_1

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