Nuprl Lemma : assert_of_dset_eq

`∀[s:DSet]. ∀[a,b:|s|].  uiff(↑(a (=b) b);a = b ∈ |s|)`

Proof

Definitions occuring in Statement :  dset: `DSet` set_eq: `=b` set_car: `|p|` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` infix_ap: `x f y` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` prop: `ℙ` infix_ap: `x f y` dset: `DSet` implies: `P `` Q` eqfun_p: `IsEqFun(T;eq)`
Lemmas referenced :  assert_wf set_eq_wf assert_witness equal_wf set_car_wf dset_wf dset_properties
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality isect_memberEquality isectElimination hypothesisEquality axiomEquality hypothesis lemma_by_obid applyEquality setElimination rename equalityTransitivity equalitySymmetry independent_functionElimination because_Cache

Latex:
\mforall{}[s:DSet].  \mforall{}[a,b:|s|].    uiff(\muparrow{}(a  (=\msubb{})  b);a  =  b)

Date html generated: 2016_05_15-PM-00_04_01
Last ObjectModification: 2015_12_26-PM-11_28_54

Theory : sets_1

Home Index