Nuprl Lemma : sq_stable_qle
∀[r,s:ℚ]. SqStable(r ≤ s)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
rationals: ℚ,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
qle: r ≤ s,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
sq_stable: SqStable(P),
implies: P ⇒ Q,
grp_leq: a ≤ b,
infix_ap: x f y,
prop: ℙ
Lemmas referenced :
sq_stable__grp_leq,
qadd_grp_wf2,
ocgrp_wf,
assert_witness,
grp_le_wf,
squash_wf,
grp_leq_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[r,s:\mBbbQ{}]. SqStable(r \mleq{} s)
Date html generated:
2016_05_15-PM-10_45_28
Last ObjectModification:
2015_12_27-PM-07_53_30
Theory : rationals
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