Nuprl Lemma : rmatrix_wf
∀[a,b:ℕ]. (ℝ(a × b) ∈ Type)
Proof
Definitions occuring in Statement :
rmatrix: ℝ(a × b),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rmatrix: ℝ(a × b),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B
Lemmas referenced :
int_seg_wf,
real_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[a,b:\mBbbN{}]. (\mBbbR{}(a \mtimes{} b) \mmember{} Type)
Date html generated:
2019_10_30-AM-08_11_04
Last ObjectModification:
2019_09_18-PM-06_43_57
Theory : reals
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