### Nuprl Lemma : rng_from_grp_wf

`∀g:GrpSig. ∀times:|g| ⟶ |g| ⟶ |g|. ∀one:|g|. ∀div:|g| ⟶ |g| ⟶ (|g|?).  (rng_from_grp(g;times;one;div) ∈ RngSig)`

Proof

Definitions occuring in Statement :  rng_from_grp: `rng_from_grp(g;times;one;div)` all: `∀x:A. B[x]` unit: `Unit` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` rng_sig: `RngSig` grp_car: `|g|` grp_sig: `GrpSig`
Definitions unfolded in proof :  rng_from_grp: `rng_from_grp(g;times;one;div)` rng_sig: `RngSig` all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  grp_car_wf grp_eq_wf grp_le_wf grp_op_wf grp_id_wf grp_inv_wf unit_wf2 bool_wf grp_sig_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation cut dependent_pairEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis because_Cache functionEquality unionEquality productEquality cumulativity

Latex:
\mforall{}g:GrpSig.  \mforall{}times:|g|  {}\mrightarrow{}  |g|  {}\mrightarrow{}  |g|.  \mforall{}one:|g|.  \mforall{}div:|g|  {}\mrightarrow{}  |g|  {}\mrightarrow{}  (|g|?).
(rng\_from\_grp(g;times;one;div)  \mmember{}  RngSig)

Date html generated: 2016_05_16-AM-08_14_41
Last ObjectModification: 2015_12_28-PM-06_09_19

Theory : polynom_1

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