Nuprl Lemma : hgrp_of_ocgrp_wf
∀[g:OGrp]. (g↓hgrp ∈ GrpSig)
Proof
Definitions occuring in Statement :
hgrp_of_ocgrp: g↓hgrp,
ocgrp: OGrp,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hgrp_of_ocgrp: g↓hgrp,
grp_sig: GrpSig,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
hgrp_car: |g|+,
all: ∀x:A. B[x]
Lemmas referenced :
hgrp_car_wf,
grp_eq_wf,
subtype_rel_dep_function,
grp_car_wf,
bool_wf,
subtype_rel_self,
grp_le_wf,
grp_op_wf2,
grp_id_wf2,
ocgrp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
sqequalRule,
lambdaEquality,
functionEquality,
independent_isectElimination,
lambdaFormation,
productEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:OGrp]. (g\mdownarrow{}hgrp \mmember{} GrpSig)
Date html generated:
2016_05_15-PM-00_14_16
Last ObjectModification:
2015_12_26-PM-11_41_12
Theory : groups_1
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