### Nuprl Lemma : seq-append-normalize

`∀[n,m:ℕ]. ∀[s1,s2:Top].  (seq-append(n;m;s1;seq-normalize(m;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` sqequal: `s ~ t`
Definitions unfolded in proof :  seq-append: `seq-append(n;m;s1;s2)` seq-normalize: `seq-normalize(n;s)` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` nat: `ℕ` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `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` 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` prop: `ℙ` subtract: `n - m` subtype_rel: `A ⊆r B` nat_plus: `ℕ+` le: `A ≤ B` has-value: `(a)↓` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep cut thin Error :lambdaFormation_alt,  introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesis setElimination rename hypothesisEquality Error :inhabitedIsType,  unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache lessCases Error :isect_memberFormation_alt,  axiomSqEquality Error :isect_memberEquality_alt,  Error :universeIsType,  independent_pairFormation voidElimination natural_numberEquality imageMemberEquality baseClosed imageElimination independent_functionElimination Error :dependent_pairFormation_alt,  Error :equalityIsType1,  promote_hyp dependent_functionElimination instantiate cumulativity addEquality Error :equalityIsType4,  intEquality multiplyEquality applyEquality Error :lambdaEquality_alt,  minusEquality Error :dependent_set_memberEquality_alt,  sqequalSqle divergentSqle callbyvalueLess baseApply closedConclusion sqleReflexivity lessExceptionCases axiomSqleEquality exceptionSqequal

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

Date html generated: 2019_06_20-AM-11_28_38
Last ObjectModification: 2018_09_28-PM-10_42_46

Theory : bar-induction

Home Index