Nuprl Lemma : qle_weakening_lt_qorder
∀[a,b:ℚ]. a ≤ b supposing 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,
guard: {T},
uimplies: b supposing a,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
qle: r ≤ s,
grp_leq: a ≤ b,
infix_ap: x f y,
implies: P ⇒ Q,
qless: r < s,
grp_lt: a < b,
set_lt: a <p b,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|
Lemmas referenced :
grp_leq_weakening_lt,
qadd_grp_wf2,
ocmon_subtype_omon,
ocgrp_subtype_ocmon,
subtype_rel_transitivity,
ocgrp_wf,
ocmon_wf,
omon_wf,
assert_witness,
grp_le_wf,
mon_subtype_grp_sig,
dmon_subtype_mon,
abdmonoid_dmon,
ocmon_subtype_abdmonoid,
abdmonoid_wf,
dmon_wf,
mon_wf,
grp_sig_wf,
istype-assert,
set_blt_wf,
oset_of_ocmon_wf0,
rationals_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
isect_memberFormation_alt,
hypothesisEquality,
independent_functionElimination,
because_Cache,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[a,b:\mBbbQ{}]. a \mleq{} b supposing a < b
Date html generated:
2020_05_20-AM-09_14_49
Last ObjectModification:
2020_02_01-AM-10_37_56
Theory : rationals
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