Nuprl Lemma : mset_sum_comm
∀s:DSet. Comm(MSet{s};λa,b. (a + b))
Proof
Definitions occuring in Statement : 
mset_sum: a + b
, 
mset: MSet{s}
, 
comm: Comm(T;op)
, 
all: ∀x:A. B[x]
, 
lambda: λx.A[x]
, 
dset: DSet
Definitions unfolded in proof : 
comm: Comm(T;op)
, 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
infix_ap: x f y
, 
mset_sum: a + b
, 
mset: MSet{s}
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
dset: DSet
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
prop: ℙ
Lemmas referenced : 
mset_wf, 
dset_wf, 
quotient-member-eq, 
list_wf, 
set_car_wf, 
permr_wf, 
permr_equiv_rel, 
append_wf, 
permr_functionality_wrt_permr, 
permr_weakening, 
append_functionality_wrt_permr, 
permr_inversion, 
append_comm
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation_alt, 
isect_memberFormation_alt, 
introduction, 
cut, 
hypothesis, 
inhabitedIsType, 
hypothesisEquality, 
sqequalHypSubstitution, 
isect_memberEquality_alt, 
isectElimination, 
thin, 
axiomEquality, 
isectIsTypeImplies, 
universeIsType, 
extract_by_obid, 
dependent_functionElimination, 
pointwiseFunctionalityForEquality, 
pertypeElimination, 
promote_hyp, 
productElimination, 
equalityTransitivity, 
equalitySymmetry, 
rename, 
setElimination, 
because_Cache, 
lambdaEquality_alt, 
independent_isectElimination, 
independent_functionElimination, 
equalityIstype, 
productIsType, 
sqequalBase
Latex:
\mforall{}s:DSet.  Comm(MSet\{s\};\mlambda{}a,b.  (a  +  b))
Date html generated:
2020_05_20-AM-09_35_39
Last ObjectModification:
2020_01_08-PM-06_00_16
Theory : mset
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