### Nuprl Lemma : seq-append0

`∀[n:ℕ]. ∀[s,t:Top].  (seq-append(n;0;s;t) ~ seq-normalize(n;s))`

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` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  seq-normalize: `seq-normalize(n;s)` seq-append: `seq-append(n;m;s1;s2)` uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` and: `P ∧ Q` cand: `A c∧ B` prop: `ℙ` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` subtract: `n - m` subtype_rel: `A ⊆r B` le: `A ≤ B` 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`
Lemmas referenced :  top_wf nat_wf less_than_wf lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int not-lt-2 less-iff-le condition-implies-le minus-add base_wf minus-one-mul add-swap minus-one-mul-top add-commutes add-associates zero-add add_functionality_wrt_le le-add-cancel 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 equal-wf-base less_sqequal
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut thin sqequalHypSubstitution hypothesis sqequalAxiom extract_by_obid isect_memberEquality isectElimination hypothesisEquality because_Cache baseApply closedConclusion baseClosed lambdaFormation productElimination independent_pairFormation addEquality natural_numberEquality unionElimination equalityElimination independent_isectElimination equalityTransitivity equalitySymmetry lessCases voidElimination voidEquality imageMemberEquality imageElimination independent_functionElimination dependent_functionElimination applyEquality lambdaEquality intEquality minusEquality dependent_pairFormation promote_hyp instantiate cumulativity impliesFunctionality productEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[s,t:Top].    (seq-append(n;0;s;t)  \msim{}  seq-normalize(n;s))

Date html generated: 2017_04_14-AM-07_27_07
Last ObjectModification: 2017_02_27-PM-02_56_22

Theory : bar-induction

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