Nuprl Lemma : vs-iso_inversion
∀[K:RngSig]. ∀[A,B:VectorSpace(K)]. (A ≅ B ⇒ B ≅ A)
Proof
Definitions occuring in Statement :
vs-iso: A ≅ B,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
vs-iso: A ≅ B,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
all: ∀x:A. B[x],
vs-map: A ⟶ B,
prop: ℙ
Lemmas referenced :
vs-point_wf,
vs-iso_wf,
vector-space_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation_alt,
hypothesisEquality,
cut,
hypothesis,
independent_pairFormation,
sqequalRule,
productIsType,
functionIsType,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
equalityIstype,
because_Cache,
applyEquality,
setElimination,
rename,
inhabitedIsType,
dependent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[A,B:VectorSpace(K)]. (A \mcong{} B {}\mRightarrow{} B \mcong{} A)
Date html generated:
2019_10_31-AM-06_27_46
Last ObjectModification:
2019_08_02-PM-04_05_11
Theory : linear!algebra
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