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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