Nuprl Lemma : mset_sum_assoc
∀s:DSet. Assoc(MSet{s};λa,b. (a + b))
Proof
Definitions occuring in Statement :
mset_sum: a + b,
mset: MSet{s},
assoc: Assoc(T;op),
all: ∀x:A. B[x],
lambda: λx.A[x],
dset: DSet
Definitions unfolded in proof :
assoc: Assoc(T;op),
infix_ap: x f y,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
mset_sum: a + b,
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
dset: DSet,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mset_wf,
dset_wf,
list_wf,
set_car_wf,
quotient-member-eq,
permr_wf,
permr_equiv_rel,
append_wf,
equal_wf,
equal-wf-base,
append_assoc,
permr_reflex,
permr_functionality_wrt_permr,
append_functionality_wrt_permr,
permr_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality,
isectElimination,
axiomEquality,
because_Cache,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
productEquality,
voidElimination,
voidEquality
Latex:
\mforall{}s:DSet. Assoc(MSet\{s\};\mlambda{}a,b. (a + b))
Date html generated:
2017_10_01-AM-09_59_06
Last ObjectModification:
2017_03_03-PM-01_00_14
Theory : mset
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