Nuprl Lemma : reqmatrix_wf
∀[a,b:ℕ]. ∀[X,Y:ℝ(a × b)]. (X ≡ Y ∈ ℙ)
Proof
Definitions occuring in Statement :
reqmatrix: X ≡ Y,
rmatrix: ℝ(a × b),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reqmatrix: X ≡ Y,
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
rmatrix: ℝ(a × b)
Lemmas referenced :
int_seg_wf,
req_wf,
rmatrix_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,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[a,b:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}(a \mtimes{} b)]. (X \mequiv{} Y \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-08_12_46
Last ObjectModification:
2019_09_19-AM-10_45_40
Theory : reals
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