Nuprl Lemma : qle_iff_lt_or_eq_qorder
∀a,b:ℚ. (a ≤ b ⇐⇒ a < b ∨ (a = b ∈ ℚ))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
qless: r < s,
qle: r ≤ s
Lemmas referenced :
grp_leq_iff_lt_or_eq,
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,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule
Latex:
\mforall{}a,b:\mBbbQ{}. (a \mleq{} b \mLeftarrow{}{}\mRightarrow{} a < b \mvee{} (a = b))
Date html generated:
2020_05_20-AM-09_14_23
Last ObjectModification:
2020_01_24-PM-07_14_23
Theory : rationals
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