Nuprl Lemma : decidable__grp_lt
∀g:OCMon. ∀a,b:|g|. Dec(a < b)
Proof
Definitions occuring in Statement :
grp_lt: a < b,
ocmon: OCMon,
grp_car: |g|,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
grp_lt: a < b
Lemmas referenced :
decidable__set_lt,
oset_of_ocmon_wf0,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
sqequalRule
Latex:
\mforall{}g:OCMon. \mforall{}a,b:|g|. Dec(a < b)
Date html generated:
2016_05_15-PM-00_12_00
Last ObjectModification:
2015_12_26-PM-11_43_01
Theory : groups_1
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