### Nuprl Lemma : seq-normalize-append

`∀[n,m:ℕ]. ∀[s1,s2:Top].  (seq-normalize(n + m;seq-append(n;m;s1;s2)) ~ seq-append(n;m;s1;s2))`

Proof

Definitions occuring in Statement :  seq-normalize: `seq-normalize(n;s)` seq-append: `seq-append(n;m;s1;s2)` nat: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` add: `n + m` sqequal: `s ~ t`
Definitions unfolded in proof :  seq-append: `seq-append(n;m;s1;s2)` seq-normalize: `seq-normalize(n;s)` has-value: `(a)↓` member: `t ∈ T` subtype_rel: `A ⊆r B` nat: `ℕ` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` and: `P ∧ Q` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` decidable: `Dec(P)` ge: `i ≥ j ` subtract: `n - m` nat_plus: `ℕ+` le: `A ≤ B`
Lemmas referenced :  set_subtype_base le_wf int_subtype_base has-value_wf_base is-exception_wf top_wf nat_wf lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int less_than_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base iff_transitivity assert_wf bnot_wf not_wf iff_weakening_uiff assert_of_bnot bottom-sqle decidable__lt exception-not-value value-type-has-value int-value-type add-commutes add_functionality_wrt_le subtract_wf le_reflexive minus-one-mul zero-add one-mul add-mul-special add-associates two-mul mul-distributes-right zero-mul less-iff-le add-zero not-lt-2 minus-one-mul-top add-swap omega-shadow mul-distributes minus-add mul-associates mul-swap nat_properties set-value-type
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep cut thin sqequalSqle divergentSqle callbyvalueLess sqequalHypSubstitution hypothesis baseApply closedConclusion baseClosed hypothesisEquality applyEquality introduction extract_by_obid isectElimination intEquality lambdaEquality natural_numberEquality independent_isectElimination productElimination lessExceptionCases axiomSqleEquality exceptionSqequal sqleReflexivity because_Cache isect_memberFormation sqequalAxiom isect_memberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry lessCases independent_pairFormation voidElimination voidEquality imageMemberEquality imageElimination independent_functionElimination setElimination rename dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity impliesFunctionality addEquality multiplyEquality minusEquality dependent_set_memberEquality

Latex:
\mforall{}[n,m:\mBbbN{}].  \mforall{}[s1,s2:Top].    (seq-normalize(n  +  m;seq-append(n;m;s1;s2))  \msim{}  seq-append(n;m;s1;s2))

Date html generated: 2017_04_14-AM-07_26_47
Last ObjectModification: 2017_02_27-PM-02_56_21

Theory : bar-induction

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