Nuprl Lemma : qless_is_sp_of_leq_a_qorder
∀[a,b:ℚ]. uiff(a < b;(a ≤ b) ∧ (¬(b ≤ a)))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q
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,
qless: r < s
Lemmas referenced :
grp_lt_is_sp_of_leq_a,
qadd_grp_wf2,
ocmon_subtype_omon,
ocgrp_subtype_ocmon,
subtype_rel_transitivity,
ocgrp_wf,
ocmon_wf,
omon_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule
Latex:
\mforall{}[a,b:\mBbbQ{}]. uiff(a < b;(a \mleq{} b) \mwedge{} (\mneg{}(b \mleq{} a)))
Date html generated:
2020_05_20-AM-09_14_26
Last ObjectModification:
2020_02_01-AM-11_22_15
Theory : rationals
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