Nuprl Lemma : real-matrix-scalar-mul_wf
∀[a,b:ℕ]. ∀[c:ℝ]. ∀[A:ℝ(a × b)]. (c*A ∈ ℝ(a × b))
Proof
Definitions occuring in Statement :
real-matrix-scalar-mul: c*A,
rmatrix: ℝ(a × b),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
rmatrix: ℝ(a × b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-matrix-scalar-mul: c*A,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat: ℕ
Lemmas referenced :
rmul_wf,
int_seg_wf,
real_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
universeIsType,
setElimination,
rename,
productElimination,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[a,b:\mBbbN{}]. \mforall{}[c:\mBbbR{}]. \mforall{}[A:\mBbbR{}(a \mtimes{} b)]. (c*A \mmember{} \mBbbR{}(a \mtimes{} b))
Date html generated:
2019_10_30-AM-08_19_15
Last ObjectModification:
2019_09_19-AM-11_58_46
Theory : reals
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