Nuprl Lemma : qle_witness
∀[r,s:ℚ]. ((r ≤ s) ⇒ (Ax ∈ r ≤ s))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
axiom: Ax
Definitions unfolded in proof :
qle: r ≤ s,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
grp_leq: a ≤ b,
infix_ap: x f y
Lemmas referenced :
grp_leq_wf,
qadd_grp_wf2,
ocgrp_wf,
rationals_wf,
assert_witness,
grp_le_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
independent_functionElimination
Latex:
\mforall{}[r,s:\mBbbQ{}]. ((r \mleq{} s) {}\mRightarrow{} (Ax \mmember{} r \mleq{} s))
Date html generated:
2016_05_15-PM-10_45_24
Last ObjectModification:
2015_12_27-PM-07_53_40
Theory : rationals
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