Nuprl Lemma : omral_plus_wf2

g:OCMon. ∀r:CDRng. ∀ps,qs:|omral(g;r)|.  (ps ++ qs ∈ |omral(g;r)|)


Proof




Definitions occuring in Statement :  omral_plus: ps ++ qs omralist: omral(g;r) all: x:A. B[x] member: t ∈ T cdrng: CDRng ocmon: OCMon set_car: |p|
Definitions unfolded in proof :  all: x:A. B[x] member: t ∈ T uall: [x:A]. B[x] subtype_rel: A ⊆B ocmon: OCMon omon: OMon so_lambda: λ2x.t[x] prop: and: P ∧ Q abmonoid: AbMon mon: Mon so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt band: p ∧b q ifthenelse: if then else fi  uiff: uiff(P;Q) uimplies: supposing a bfalse: ff infix_ap: y so_apply: x[s] cand: c∧ B omralist: omral(g;r) omral_plus: ps ++ qs
Lemmas referenced :  oal_merge_wf2 oset_of_ocmon_wf subtype_rel_sets abmonoid_wf ulinorder_wf grp_car_wf assert_wf infix_ap_wf bool_wf grp_le_wf equal_wf grp_eq_wf eqtt_to_assert cancel_wf grp_op_wf uall_wf monot_wf cdrng_is_abdmonoid cdrng_wf ocmon_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin isectElimination hypothesisEquality applyEquality sqequalRule instantiate hypothesis because_Cache lambdaEquality productEquality setElimination rename cumulativity universeEquality functionEquality unionElimination equalityElimination productElimination independent_isectElimination equalityTransitivity equalitySymmetry independent_functionElimination setEquality independent_pairFormation

Latex:
\mforall{}g:OCMon.  \mforall{}r:CDRng.  \mforall{}ps,qs:|omral(g;r)|.    (ps  ++  qs  \mmember{}  |omral(g;r)|)



Date html generated: 2017_10_01-AM-10_05_12
Last ObjectModification: 2017_03_03-PM-01_11_06

Theory : polynom_3


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