### Nuprl Lemma : alg_from_rng_wf

`∀A:Type. ∀r:RngSig. ∀act:A ⟶ |r| ⟶ |r|.  (alg_from_rng(A;r;act) ∈ algebra_sig{i:l}(A))`

Proof

Definitions occuring in Statement :  alg_from_rng: `alg_from_rng(A;r;act)` algebra_sig: `algebra_sig{i:l}(A)` all: `∀x:A. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type` rng_car: `|r|` rng_sig: `RngSig`
Definitions unfolded in proof :  alg_from_rng: `alg_from_rng(A;r;act)` algebra_sig: `algebra_sig{i:l}(A)` all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  rng_car_wf rng_eq_wf rng_le_wf rng_plus_wf rng_zero_wf rng_minus_wf rng_times_wf rng_one_wf rng_div_wf unit_wf2 bool_wf rng_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 cumulativity productEquality unionEquality universeEquality

Latex:
\mforall{}A:Type.  \mforall{}r:RngSig.  \mforall{}act:A  {}\mrightarrow{}  |r|  {}\mrightarrow{}  |r|.    (alg\_from\_rng(A;r;act)  \mmember{}  algebra\_sig\{i:l\}(A))

Date html generated: 2016_05_16-AM-08_14_44
Last ObjectModification: 2015_12_28-PM-06_09_15

Theory : polynom_1

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