Nuprl Lemma : eq_mset_wf

s:DSet. ∀a,b:MSet{s}.  (eq_mset{s}(a,b) ∈ 𝔹)


Proof




Definitions occuring in Statement :  eq_mset: eq_mset{s}(a,b) mset: MSet{s} bool: 𝔹 all: x:A. B[x] member: t ∈ T dset: DSet
Definitions unfolded in proof :  all: x:A. B[x] member: t ∈ T eq_mset: eq_mset{s}(a,b) mset: MSet{s} quotient: x,y:A//B[x; y] and: P ∧ Q uall: [x:A]. B[x] dset: DSet prop: uimplies: supposing a iff: ⇐⇒ Q implies:  Q rev_implies:  Q
Lemmas referenced :  mset_wf dset_wf bool_wf equal-wf-base list_wf set_car_wf permr_wf iff_imp_equal_bool bpermr_wf assert_of_bpermr assert_wf iff_wf permr_functionality_wrt_permr
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalHypSubstitution hypothesis lemma_by_obid dependent_functionElimination thin hypothesisEquality pointwiseFunctionalityForEquality sqequalRule pertypeElimination productElimination productEquality isectElimination setElimination rename because_Cache independent_isectElimination addLevel independent_pairFormation impliesFunctionality equalityTransitivity equalitySymmetry independent_functionElimination

Latex:
\mforall{}s:DSet.  \mforall{}a,b:MSet\{s\}.    (eq\_mset\{s\}(a,b)  \mmember{}  \mBbbB{})



Date html generated: 2016_05_16-AM-07_46_54
Last ObjectModification: 2015_12_28-PM-06_03_34

Theory : mset


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