Nuprl Lemma : qless_trichot_qorder
∀a,b:ℚ. (a < b ∨ (a = b ∈ ℚ) ∨ b < a)
Proof
Definitions occuring in Statement :
qless: r < s,
rationals: ℚ,
all: ∀x:A. B[x],
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
qless: r < s,
guard: {T}
Lemmas referenced :
grp_lt_trichot,
qadd_grp_wf2,
ocgrp_subtype_ocmon,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
sqequalRule,
inhabitedIsType,
hypothesisEquality,
universeIsType
Latex:
\mforall{}a,b:\mBbbQ{}. (a < b \mvee{} (a = b) \mvee{} b < a)
Date html generated:
2020_05_20-AM-09_15_04
Last ObjectModification:
2020_01_27-AM-09_32_52
Theory : rationals
Home
Index