Nuprl Lemma : assert_of_mon_eq

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


Proof




Definitions occuring in Statement :  dmon: DMon grp_eq: =b grp_car: |g| assert: b uiff: uiff(P;Q) uall: [x:A]. B[x] infix_ap: y equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a prop: infix_ap: y dmon: DMon mon: Mon implies:  Q eqfun_p: IsEqFun(T;eq)
Lemmas referenced :  assert_wf grp_eq_wf assert_witness equal_wf grp_car_wf dmon_wf dmon_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:DMon].  \mforall{}[a,b:|s|].    uiff(\muparrow{}(a  =\msubb{}  b);a  =  b)



Date html generated: 2016_05_15-PM-00_07_04
Last ObjectModification: 2015_12_26-PM-11_47_00

Theory : groups_1


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