Nuprl Lemma : grp_op_wf2
∀[g:OGrp]. (* ∈ |g|+ ⟶ |g|+ ⟶ |g|+)
Proof
Definitions occuring in Statement :
hgrp_car: |g|+,
ocgrp: OGrp,
grp_op: *,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
hgrp_car: |g|+,
prop: ℙ,
uimplies: b supposing a,
infix_ap: x f y
Lemmas referenced :
grp_op_wf,
hgrp_car_wf,
ocgrp_wf,
hgrp_car_properties,
grp_leq_wf,
grp_id_wf,
grp_op_polarity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
functionExtensionality,
applyEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
dependent_set_memberEquality,
independent_isectElimination
Latex:
\mforall{}[g:OGrp]. (* \mmember{} |g|\msupplus{} {}\mrightarrow{} |g|\msupplus{} {}\mrightarrow{} |g|\msupplus{})
Date html generated:
2016_05_15-PM-00_14_07
Last ObjectModification:
2015_12_26-PM-11_41_09
Theory : groups_1
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