Nuprl Lemma : gcopower_wf
∀s:DSet. ∀g:AbGrp. (gcopower{i}(s;g) ∈ 𝕌')
Proof
Definitions occuring in Statement :
gcopower: gcopower{i}(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
abgrp: AbGrp,
dset: DSet
Definitions unfolded in proof :
gcopower: gcopower{i}(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
monoid_hom: MonHom(M1,M2)
Lemmas referenced :
gcopower_sig_wf,
eqfun_p_wf,
grp_car_wf,
gcopower_grp_wf,
grp_eq_wf,
grp_p_wf,
comm_wf,
grp_op_wf,
all_wf,
set_car_wf,
monoid_hom_p_wf,
gcopower_inj_wf,
abgrp_wf,
monoid_hom_wf,
uni_sat_wf,
gcopower_umap_wf,
subtype_rel_dep_function,
equal_wf,
compose_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productEquality,
cumulativity,
isectElimination,
because_Cache,
lambdaEquality,
applyEquality,
instantiate,
functionEquality,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}g:AbGrp. (gcopower\{i\}(s;g) \mmember{} \mBbbU{}')
Date html generated:
2016_05_16-AM-08_14_03
Last ObjectModification:
2015_12_28-PM-06_09_34
Theory : polynom_1
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