Nuprl Lemma : grp_op_preserves_le_qorder
∀[x,y,z:ℚ]. (x + y) ≤ (x + z) supposing y ≤ z
Proof
Definitions occuring in Statement :
qle: 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,
qle: r ≤ s
Lemmas referenced :
grp_op_preserves_le,
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{}[x,y,z:\mBbbQ{}]. (x + y) \mleq{} (x + z) supposing y \mleq{} z
Date html generated:
2020_05_20-AM-09_15_08
Last ObjectModification:
2020_02_04-PM-01_42_05
Theory : rationals
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