Nuprl Lemma : mset_diff_wf
∀s:DSet. ∀a,b:MSet{s}. (a - b ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_diff: a - b,
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
mset_diff: a - b,
all: ∀x:A. B[x],
member: t ∈ T,
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
quotient-member-eq,
list_wf,
set_car_wf,
permr_wf,
permr_equiv_rel,
diff_wf,
equal-wf-base,
mset_wf,
dset_wf,
diff_functionality_wrt_permr
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
pertypeElimination,
productElimination,
thin,
lemma_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
independent_functionElimination,
productEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. (a - b \mmember{} MSet\{s\})
Date html generated:
2016_05_16-AM-07_49_01
Last ObjectModification:
2015_12_28-PM-06_02_23
Theory : mset
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