Nuprl Lemma : sq_stable__r2-left-or
∀a,b,c:ℝ^2. SqStable(r2-left(a;b;c) ∨ r2-left(a;c;b))
Proof
Definitions occuring in Statement :
r2-left: r2-left(p;q;r),
real-vec: ℝ^n,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
or: P ∨ Q,
natural_number: $n
Definitions unfolded in proof :
r2-left: r2-left(p;q;r),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
sq_stable__rless-or2,
int-to-real_wf,
r2-det_wf,
real-vec_wf,
istype-void,
istype-le
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
because_Cache,
inhabitedIsType,
universeIsType,
dependent_set_memberEquality_alt,
independent_pairFormation,
voidElimination
Latex:
\mforall{}a,b,c:\mBbbR{}\^{}2. SqStable(r2-left(a;b;c) \mvee{} r2-left(a;c;b))
Date html generated:
2019_10_30-AM-08_54_29
Last ObjectModification:
2019_10_10-AM-10_15_57
Theory : reals
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