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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