Nuprl Lemma : hgrp_car_properties
∀[g:GrpSig]. ∀[x:|g|+]. (e ≤ x)
Proof
Definitions occuring in Statement :
hgrp_car: |g|+,
grp_leq: a ≤ b,
grp_id: e,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hgrp_car: |g|+,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
grp_leq: a ≤ b,
infix_ap: x f y
Lemmas referenced :
grp_sig_wf,
hgrp_car_wf,
grp_le_wf,
assert_witness,
grp_id_wf,
sq_stable__grp_leq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:GrpSig]. \mforall{}[x:|g|\msupplus{}]. (e \mleq{} x)
Date html generated:
2016_05_15-PM-00_14_04
Last ObjectModification:
2016_01_15-PM-11_05_06
Theory : groups_1
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