### Nuprl Lemma : seq-normalize0

`seq-normalize(0;λm.⊥) ~ λm.eval x = m in`
`                           ⊥`

Proof

Definitions occuring in Statement :  seq-normalize: `seq-normalize(n;s)` bottom: `⊥` callbyvalue: callbyvalue lambda: `λx.A[x]` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  seq-normalize: `seq-normalize(n;s)` has-value: `(a)↓` member: `t ∈ T` and: `P ∧ Q` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` 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` 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`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf bottom-sqle 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 exception-not-value value-type-has-value int-value-type has-value_wf_base is-exception_wf bottom_diverge exception-not-bottom
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity sqequalRule sqequalSqle cut divergentSqle callbyvalueLess sqequalHypSubstitution hypothesis baseApply closedConclusion baseClosed hypothesisEquality thin productElimination introduction extract_by_obid isectElimination lambdaFormation unionElimination equalityElimination because_Cache independent_isectElimination equalityTransitivity equalitySymmetry lessCases isect_memberFormation sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality natural_numberEquality imageMemberEquality imageElimination independent_functionElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity impliesFunctionality lessExceptionCases axiomSqleEquality intEquality exceptionSqequal sqleReflexivity callbyvalueCallbyvalue callbyvalueReduce callbyvalueExceptionCases

Latex:
seq-normalize(0;\mlambda{}m.\mbot{})  \msim{}  \mlambda{}m.eval  x  =  m  in
\mbot{}

Date html generated: 2017_04_14-AM-07_26_50
Last ObjectModification: 2017_02_27-PM-02_56_07

Theory : bar-induction

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