Nuprl Lemma : q-square-non-neg
∀[q:ℚ]. (0 ≤ (q * q))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qmul: r * s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
guard: {T},
cand: A c∧ B
Lemmas referenced :
qle_witness,
int-subtype-rationals,
qmul_wf,
rationals_wf,
qless_wf,
or_wf,
and_wf,
equal_wf,
qmul-non-neg,
qminus-positive,
qless_trichot_qorder
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
applyEquality,
sqequalRule,
hypothesisEquality,
independent_functionElimination,
because_Cache,
minusEquality,
dependent_functionElimination,
productElimination,
addLevel,
orFunctionality,
independent_pairFormation,
independent_isectElimination,
andLevelFunctionality,
unionElimination,
inrFormation,
inlFormation,
equalitySymmetry
Latex:
\mforall{}[q:\mBbbQ{}]. (0 \mleq{} (q * q))
Date html generated:
2016_05_15-PM-10_58_57
Last ObjectModification:
2015_12_27-PM-07_50_26
Theory : rationals
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