Nuprl Lemma : oal_hgp_wf
∀s:LOSet. ∀g:OGrp. (oal_hgp(s;g) ∈ GrpSig)
Proof
Definitions occuring in Statement :
oal_hgp: oal_hgp(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
ocgrp: OGrp,
grp_sig: GrpSig,
loset: LOSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
oal_hgp: oal_hgp(s;g),
grp_sig: GrpSig,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
hgrp_of_ocgrp_wf2,
set_car_wf,
oalist_wf,
ocmon_subtype_abdmonoid,
set_eq_wf,
oal_ble_wf,
ocgrp_subtype_abdgrp,
set_car_inc,
oal_merge_wf2,
oal_nil_wf,
bool_wf,
ocgrp_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_pairEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
because_Cache,
lambdaEquality,
functionEquality,
productEquality,
cumulativity
Latex:
\mforall{}s:LOSet. \mforall{}g:OGrp. (oal\_hgp(s;g) \mmember{} GrpSig)
Date html generated:
2016_05_16-AM-08_22_21
Last ObjectModification:
2015_12_28-PM-06_25_01
Theory : polynom_2
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