Nuprl Lemma : grp_leq_iff_lt_or_eq
∀g:OMon. ∀a,b:|g|. (a ≤ b ⇐⇒ (a < b) ∨ (a = b ∈ |g|))
Proof
Definitions occuring in Statement :
grp_lt: a < b,
grp_leq: a ≤ b,
omon: OMon,
grp_car: |g|,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
loset: LOSet,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
set_leq: a ≤ b,
set_le: ≤b,
pi2: snd(t),
grp_leq: a ≤ b,
grp_lt: a < b
Lemmas referenced :
set_leq_iff_lt_or_eq,
oset_of_ocmon_wf,
loset_wf,
omon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule
Latex:
\mforall{}g:OMon. \mforall{}a,b:|g|. (a \mleq{} b \mLeftarrow{}{}\mRightarrow{} (a < b) \mvee{} (a = b))
Date html generated:
2016_05_15-PM-00_11_57
Last ObjectModification:
2015_12_26-PM-11_43_18
Theory : groups_1
Home
Index