Nuprl Lemma : qle_transitivity_qorder
∀[a,b,c:ℚ]. (a ≤ c) supposing ((b ≤ c) and (a ≤ b))
Proof
Definitions occuring in Statement :
qle: 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),
qle: r ≤ s
Lemmas referenced :
grp_leq_transitivity,
qadd_grp_wf2,
ocgrp_subtype_ocmon
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
sqequalRule
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. (a \mleq{} c) supposing ((b \mleq{} c) and (a \mleq{} b))
Date html generated:
2020_05_20-AM-09_14_51
Last ObjectModification:
2020_01_28-PM-04_20_58
Theory : rationals
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