### Nuprl Lemma : fps-div-one

`∀[X:Type]`
`  ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[f:PowerSeries(X;r)].  ((f÷1) = f ∈ PowerSeries(X;r)) supposing valueall-type(X)`

Proof

Definitions occuring in Statement :  fps-div: `(f÷g)` fps-one: `1` power-series: `PowerSeries(X;r)` deq: `EqDecider(T)` valueall-type: `valueall-type(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T` crng: `CRng` rng_one: `1`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` crng: `CRng` rng: `Rng` and: `P ∧ Q` cand: `A c∧ B` all: `∀x:A. B[x]` true: `True` squash: `↓T` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` implies: `P `` Q` fps-coeff: `f[b]` fps-one: `1` ifthenelse: `if b then t else f fi ` bag-null: `bag-null(bs)` null: `null(as)` empty-bag: `{}` nil: `[]` it: `⋅` btrue: `tt` rng_one: `1` pi1: `fst(t)` pi2: `snd(t)`
Lemmas referenced :  power-series_wf crng_wf deq_wf valueall-type_wf fps-one_wf rng_one_wf fps-div-unique equal_wf squash_wf true_wf mul_one_fps iff_weakening_equal rng_car_wf rng_times_one bag_null_empty_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut equalitySymmetry hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity universeEquality setElimination rename independent_pairFormation independent_isectElimination dependent_functionElimination natural_numberEquality applyEquality lambdaEquality imageElimination productElimination imageMemberEquality baseClosed independent_functionElimination

Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)].  \mforall{}[r:CRng].  \mforall{}[f:PowerSeries(X;r)].    ((f\mdiv{}1)  =  f)  supposing  valueall-type(X)

Date html generated: 2018_05_21-PM-09_57_51
Last ObjectModification: 2017_07_26-PM-06_33_29

Theory : power!series

Home Index