Nuprl Lemma : rat-cube-complex-polyhedron_functionality
∀[k:ℕ]. ∀[K,L:ℚCube(k) List]. |K| ≡ |L| supposing permutation(ℚCube(k);K;L)
Proof
Definitions occuring in Statement :
rat-cube-complex-polyhedron: |K|,
permutation: permutation(T;L1;L2),
list: T List,
nat: ℕ,
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
rational-cube: ℚCube(k)
Definitions unfolded in proof :
false: False,
cand: A c∧ B,
exists: ∃x:A. B[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
not: ¬A,
rat-cube-complex-polyhedron: |K|,
subtype_rel: A ⊆r B,
and: P ∧ Q,
ext-eq: A ≡ B,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
list_wf,
permutation_wf,
rat-cube-complex-polyhedron_wf,
istype-void,
l_exists_wf,
l_member_wf,
in-rat-cube_wf,
l_exists_iff,
rational-cube_wf,
member-permutation
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
independent_pairEquality,
functionIsType,
voidElimination,
productIsType,
promote_hyp,
dependent_pairFormation_alt,
productElimination,
universeIsType,
setIsType,
sqequalRule,
because_Cache,
lambdaFormation_alt,
dependent_set_memberEquality_alt,
rename,
setElimination,
lambdaEquality_alt,
independent_pairFormation,
independent_functionElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[K,L:\mBbbQ{}Cube(k) List]. |K| \mequiv{} |L| supposing permutation(\mBbbQ{}Cube(k);K;L)
Date html generated:
2019_11_04-PM-04_43_40
Last ObjectModification:
2019_11_02-PM-10_48_02
Theory : real!vectors
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