### Nuprl Lemma : fma_from_gcp_wf

g:GrpSig. ∀r:RngSig. ∀c:gcopower_sig{i:l}(g↓set;r↓+gp). ∀a:algebra{i:l}(r).
(((a↓grp) c.grp ∈ GrpSig)  (fma_from_gcp(g;r;c;a) ∈ fma_sig{i:l}(g;r)))

Proof

Definitions occuring in Statement :  fma_from_gcp: fma_from_gcp(g;r;c;a) fma_sig: fma_sig{i:l}(G;A) gcopower_grp: g1.grp gcopower_sig: gcopower_sig{i:l}(s;g) algebra: algebra{i:l}(A) grp_of_module: m↓grp all: x:A. B[x] implies:  Q member: t ∈ T equal: t ∈ T add_grp_of_rng: r↓+gp rng_sig: RngSig dset_of_mon: g↓set grp_sig: GrpSig
Definitions unfolded in proof :  fma_from_gcp: fma_from_gcp(g;r;c;a) fma_sig: fma_sig{i:l}(G;A) all: x:A. B[x] implies:  Q member: t ∈ T uall: [x:A]. B[x] algebra: algebra{i:l}(A) module: A-Module prop: tlambda: λx:T. b[x] grp_of_module: m↓grp add_grp_of_rng: r↓+gp grp_car: |g| pi1: fst(t) rng_of_alg: a↓rg rng_car: |r| squash: T true: True label: ...\$L... t dset_of_mon: g↓set set_car: |p| subtype_rel: A ⊆B guard: {T} uimplies: supposing a
Lemmas referenced :  set_car_wf alg_act_wf grp_of_module_wf2 gcopower_umap_wf ext-eq_weakening subtype_rel_weakening rng_one_wf gcopower_inj_wf true_wf squash_wf rng_sig_wf gcopower_sig_wf add_grp_of_rng_wf dset_of_mon_wf0 gcopower_grp_wf grp_of_module_wf grp_sig_wf equal_wf rng_car_wf alg_car_wf grp_car_wf algebra_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation cut dependent_pairEquality functionEquality lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality hypothesis cumulativity isectElimination setElimination rename productEquality instantiate lambdaEquality applyEquality imageElimination equalityTransitivity equalitySymmetry natural_numberEquality imageMemberEquality baseClosed independent_isectElimination because_Cache

Latex:
\mforall{}g:GrpSig.  \mforall{}r:RngSig.  \mforall{}c:gcopower\_sig\{i:l\}(g\mdownarrow{}set;r\mdownarrow{}+gp).  \mforall{}a:algebra\{i:l\}(r).
(((a\mdownarrow{}grp)  =  c.grp)  {}\mRightarrow{}  (fma\_from\_gcp(g;r;c;a)  \mmember{}  fma\_sig\{i:l\}(g;r)))

Date html generated: 2016_05_16-AM-08_14_50
Last ObjectModification: 2016_01_16-PM-11_41_54

Theory : polynom_1

Home Index