Nuprl Lemma : add-ipoly-req
∀p,q:iMonomial() List. ipolynomial-term(add-ipoly(p;q)) ≡ ipolynomial-term(p) (+) ipolynomial-term(q)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
add-ipoly: add-ipoly(p;q),
ipolynomial-term: ipolynomial-term(p),
iMonomial: iMonomial(),
itermAdd: left (+) right,
list: T List,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
req_int_terms: t1 ≡ t2,
le: A ≤ B,
less_than': less_than'(a;b),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
uiff: uiff(P;Q),
add-ipoly: add-ipoly(p;q),
has-value: (a)↓,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bfalse: ff,
ipolynomial-term: ipolynomial-term(p),
real_term_value: real_term_value(f;t),
itermAdd: left (+) right,
int_term_ind: int_term_ind,
itermConstant: "const",
rev_uimplies: rev_uimplies(P;Q),
bool: 𝔹,
unit: Unit,
it: ⋅,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
iMonomial: iMonomial(),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
int_nzero: ℤ-o,
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a),
pi1: fst(t),
nequal: a ≠ b ∈ T ,
imonomial-le: imonomial-le(m1;m2),
pi2: snd(t),
squash: ↓T
Latex:
\mforall{}p,q:iMonomial() List.
ipolynomial-term(add-ipoly(p;q)) \mequiv{} ipolynomial-term(p) (+) ipolynomial-term(q)
Date html generated:
2020_05_20-AM-10_54_13
Last ObjectModification:
2020_01_02-PM-02_09_10
Theory : reals
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