Nuprl Lemma : fabgrp_wf
∀s:DSet. (FAbGrp(s) ∈ 𝕌')
Proof
Definitions occuring in Statement :
fabgrp: FAbGrp(s),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
dset: DSet
Definitions unfolded in proof :
fabgrp: FAbGrp(s),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
dset: DSet,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
fabgrp_sig_wf,
all_wf,
abgrp_wf,
set_car_wf,
grp_car_wf,
uni_sat_wf,
fabgrp_grp_wf,
fabgrp_umap_wf,
monoid_hom_p_wf,
equal_wf,
compose_wf,
fabgrp_inj_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
setEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
isectElimination,
lambdaEquality,
functionEquality,
setElimination,
rename,
because_Cache,
applyEquality,
functionExtensionality,
productEquality,
cumulativity,
universeEquality
Latex:
\mforall{}s:DSet. (FAbGrp(s) \mmember{} \mBbbU{}')
Date html generated:
2017_10_01-AM-10_01_20
Last ObjectModification:
2017_03_03-PM-01_03_40
Theory : polynom_1
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