### Nuprl Lemma : make-strict-agrees

`∀[alpha:ℕ ⟶ ℕ]. ∀[n:ℕ].  ∀[i:ℕn]. ((make-strict(alpha) i) = (alpha i) ∈ ℤ) supposing strictly-increasing-seq(n;alpha)`

Proof

Definitions occuring in Statement :  make-strict: `make-strict(alpha)` strictly-increasing-seq: `strictly-increasing-seq(n;s)` int_seg: `{i..j-}` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` apply: `f a` function: `x:A ⟶ B[x]` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` implies: `P `` Q` all: `∀x:A. B[x]` nat: `ℕ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` prop: `ℙ` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` strictly-increasing-seq: `strictly-increasing-seq(n;s)` make-strict: `make-strict(alpha)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` rev_implies: `P `` Q` iff: `P `⇐⇒` Q` strict-inc: `StrictInc` squash: `↓T` true: `True`
Lemmas referenced :  int_seg_wf strictly-increasing-seq_wf subtype_rel_dep_function nat_wf int_seg_subtype_nat istype-false istype-nat nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf istype-less_than int_seg_properties decidable__le intformnot_wf int_formula_prop_not_lemma istype-le subtract-1-ge-0 decidable__lt itermSubtract_wf int_term_value_subtract_lemma subtract_wf primrec-unroll lt_int_wf eqtt_to_assert assert_of_lt_int decidable__equal_int intformeq_wf int_formula_prop_eq_lemma eqff_to_assert bool_cases_sqequal subtype_base_sq bool_wf bool_subtype_base assert-bnot iff_weakening_uiff assert_wf less_than_wf subtract-add-cancel make-strict_wf squash_wf true_wf subtype_rel_self iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut thin sqequalHypSubstitution independent_functionElimination hypothesis dependent_functionElimination hypothesisEquality Error :universeIsType,  extract_by_obid isectElimination natural_numberEquality setElimination rename sqequalRule Error :isect_memberEquality_alt,  axiomEquality Error :isectIsTypeImplies,  Error :inhabitedIsType,  applyEquality Error :lambdaEquality_alt,  intEquality independent_isectElimination because_Cache independent_pairFormation Error :lambdaFormation_alt,  Error :functionIsType,  intWeakElimination approximateComputation Error :dependent_pairFormation_alt,  int_eqEquality voidElimination Error :functionIsTypeImplies,  productElimination Error :dependent_set_memberEquality_alt,  unionElimination Error :productIsType,  equalityElimination equalityTransitivity equalitySymmetry Error :equalityIstype,  promote_hyp instantiate cumulativity imageElimination imageMemberEquality baseClosed universeEquality

Latex:
\mforall{}[alpha:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}].  \mforall{}[n:\mBbbN{}].
\mforall{}[i:\mBbbN{}n].  ((make-strict(alpha)  i)  =  (alpha  i))  supposing  strictly-increasing-seq(n;alpha)

Date html generated: 2019_06_20-PM-02_57_20
Last ObjectModification: 2019_02_06-PM-03_51_03

Theory : continuity

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