Nuprl Lemma : q_less_wf
∀[a,b:ℚ]. (q_less(a;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
q_less: q_less(r;s),
rationals: ℚ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q_less: q_less(r;s),
subtype_rel: A ⊆r B,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
qadd_grp: <ℚ+>,
grp_car: |g|
Lemmas referenced :
rational_set_blt,
set_blt_wf,
oset_of_ocmon_wf0,
qadd_grp_wf2,
ocgrp_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbQ{}]. (q\_less(a;b) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-10_57_22
Last ObjectModification:
2015_12_27-PM-07_52_04
Theory : rationals
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