Nuprl Lemma : q-square-positive
∀[q:ℚ]. 0 < q * q supposing ¬(q = 0 ∈ ℚ)
Proof
Definitions occuring in Statement :
qless: r < s,
qmul: r * s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
not: ¬A,
false: False,
rev_implies: P ⇐ Q
Lemmas referenced :
q-square-non-neg,
qless_witness,
qmul_wf,
not_wf,
equal_wf,
rationals_wf,
qle_iff_lt_or_eq_qorder,
int-subtype-rationals,
qmul-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productElimination,
unionElimination,
voidElimination
Latex:
\mforall{}[q:\mBbbQ{}]. 0 < q * q supposing \mneg{}(q = 0)
Date html generated:
2016_05_15-PM-10_59_02
Last ObjectModification:
2015_12_27-PM-07_51_06
Theory : rationals
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