Nuprl Lemma : qless_transitivity_2_qorder
∀[a,b,c:ℚ]. (a < c) supposing ((b ≤ c) and a < b)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
qless: r < s,
uimplies: b supposing a,
grp_lt: a < b,
set_lt: a <p b,
guard: {T},
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
implies: P ⇒ Q,
qle: r ≤ s,
grp_leq: a ≤ b,
infix_ap: x f y
Lemmas referenced :
grp_lt_transitivity_2,
qadd_grp_wf2,
ocgrp_subtype_ocmon,
assert_witness,
set_blt_wf,
oset_of_ocmon_wf0,
mon_subtype_grp_sig,
dmon_subtype_mon,
abdmonoid_dmon,
ocmon_subtype_abdmonoid,
subtype_rel_transitivity,
ocgrp_wf,
ocmon_wf,
abdmonoid_wf,
dmon_wf,
mon_wf,
grp_sig_wf,
istype-assert,
grp_le_wf,
rationals_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
sqequalRule,
isect_memberFormation_alt,
instantiate,
independent_isectElimination,
hypothesisEquality,
independent_functionElimination,
because_Cache,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. (a < c) supposing ((b \mleq{} c) and a < b)
Date html generated:
2020_05_20-AM-09_14_37
Last ObjectModification:
2020_02_03-PM-02_48_17
Theory : rationals
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