Nuprl Lemma : grp_op_preserves_lt_qorder
∀[u,v,w:ℚ]. u + v < u + w supposing v < w
Proof
Definitions occuring in Statement :
qless: r < s,
qadd: 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),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
qless: r < s
Lemmas referenced :
grp_op_preserves_lt,
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{}[u,v,w:\mBbbQ{}]. u + v < u + w supposing v < w
Date html generated:
2020_05_20-AM-09_15_11
Last ObjectModification:
2020_01_25-AM-11_22_14
Theory : rationals
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