### Nuprl Lemma : make-strict_wf

`∀[alpha:ℕ ⟶ ℕ]. (make-strict(alpha) ∈ StrictInc)`

Proof

Definitions occuring in Statement :  make-strict: `make-strict(alpha)` strict-inc: `StrictInc` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` make-strict: `make-strict(alpha)` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` int_seg: `{i..j-}` guard: `{T}` ge: `i ≥ j ` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` subtype_rel: `A ⊆r B` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` primrec: `primrec(n;b;c)` less_than: `a < b` squash: `↓T`
Lemmas referenced :  primrec_wf nat_wf false_wf le_wf lt_int_wf nat_properties int_seg_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_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_add_lemma int_term_value_var_lemma int_formula_prop_wf bool_wf eqtt_to_assert assert_of_lt_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf int_seg_wf implies-strict-inc intformless_wf int_formula_prop_less_lemma ge_wf member-less_than primrec1_lemma subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtract-add-cancel primrec0_lemma decidable__lt primrec-unroll add-subtract-cancel le_weakening2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lambdaEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality applyEquality functionExtensionality because_Cache dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation setElimination rename addEquality productElimination dependent_functionElimination unionElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality equalityElimination equalityTransitivity equalitySymmetry promote_hyp instantiate cumulativity axiomEquality functionEquality intWeakElimination imageElimination

Latex:
\mforall{}[alpha:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}].  (make-strict(alpha)  \mmember{}  StrictInc)

Date html generated: 2018_05_21-PM-01_20_31
Last ObjectModification: 2018_05_19-AM-06_33_20

Theory : continuity

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