`∀[r:CRng]. ∀[p,q:mv-polynomial(r)].  (mvp-add(r;p;q) ∈ mv-polynomial(r))`

Proof

Definitions occuring in Statement :  mvp-add: `mvp-add(r;p;q)` mv-polynomial: `mv-polynomial(r)` uall: `∀[x:A]. B[x]` member: `t ∈ T` crng: `CRng`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` mvp-add: `mvp-add(r;p;q)` mv-polynomial: `mv-polynomial(r)` prop: `ℙ` fps-support: `fps-support(r;f;s)` uimplies: `b supposing a` fps-add: `(f+g)` fps-coeff: `f[b]` crng: `CRng` rng: `Rng` not: `¬A` implies: `P `` Q` all: `∀x:A. B[x]` or: `P ∨ Q` false: `False` guard: `{T}` true: `True` squash: `↓T` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` ring_p: `IsRing(T;plus;zero;neg;times;one)` group_p: `IsGroup(T;op;id;inv)` monoid_p: `IsMonoid(T;op;id)` assoc: `Assoc(T;op)` ident: `Ident(T;op;id)` infix_ap: `x f y`
Lemmas referenced :  bag-lub_wf atom-deq_wf fps-add_wf fps-support_wf power-series_wf mv-polynomial_wf crng_wf not_wf sub-bag_wf bag_wf rng_car_wf rng_plus_wf sub-bag-lub rng_zero_wf equal_wf squash_wf true_wf iff_weakening_equal crng_properties rng_properties
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin dependent_pairEquality extract_by_obid isectElimination atomEquality hypothesis hypothesisEquality dependent_set_memberEquality setElimination rename because_Cache setEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality lambdaFormation independent_functionElimination dependent_functionElimination inlFormation voidElimination inrFormation natural_numberEquality applyEquality lambdaEquality imageElimination universeEquality independent_isectElimination imageMemberEquality baseClosed

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