Nuprl Lemma : assert_of_eq_mset
∀s:DSet. ∀a,b:MSet{s}. (↑eq_mset{s}(a,b) ⇐⇒ a = b ∈ MSet{s})
Proof
Definitions occuring in Statement :
eq_mset: eq_mset{s}(a,b),
mset: MSet{s},
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
mset: MSet{s},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
prop: ℙ,
quotient: x,y:A//B[x; y],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
dset: DSet,
so_apply: x[s1;s2],
uimplies: b supposing a,
squash: ↓T,
eq_mset: eq_mset{s}(a,b)
Lemmas referenced :
member_wf,
and_wf,
assert_of_bpermr,
quotient-member-eq,
bpermr_wf,
equal-wf-base,
permr_equiv_rel,
list_wf,
set_car_wf,
permr_wf,
subtype_quotient,
iff_wf,
squash_wf,
sq_stable__equal,
decidable__assert,
sq_stable_from_decidable,
equal_wf,
eq_mset_wf,
assert_wf,
sq_stable__iff,
dset_wf,
mset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
independent_functionElimination,
because_Cache,
introduction,
pointwiseFunctionalityForEquality,
sqequalRule,
pertypeElimination,
productElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
productEquality,
imageMemberEquality,
baseClosed,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
imageElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. (\muparrow{}eq\_mset\{s\}(a,b) \mLeftarrow{}{}\mRightarrow{} a = b)
Date html generated:
2016_05_16-AM-07_46_58
Last ObjectModification:
2016_01_16-PM-11_40_19
Theory : mset
Home
Index