Nuprl Lemma : proj-rev_wf
∀[n:ℕ]. ∀[p:ℙ^n].  (proj-rev(n;p) ∈ ℙ^n)
Proof
Definitions occuring in Statement : 
proj-rev: proj-rev(n;p)
, 
real-proj: ℙ^n
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
real-proj: ℙ^n
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
real-vec: ℝ^n
, 
so_apply: x[s]
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
proj-rev: proj-rev(n;p)
, 
int_seg: {i..j-}
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
not: ¬A
Lemmas referenced : 
exists_wf, 
int_seg_wf, 
rneq_wf, 
int-to-real_wf, 
real-proj_wf, 
nat_wf, 
ifthenelse_wf, 
lt_int_wf, 
real_wf, 
rminus_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_lt_int, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
less_than_wf, 
rminus-neq-zero
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
dependent_set_memberEquality, 
extract_by_obid, 
isectElimination, 
natural_numberEquality, 
addEquality, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
productElimination, 
dependent_pairFormation, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
independent_isectElimination, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
cumulativity, 
independent_functionElimination, 
voidElimination
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[p:\mBbbP{}\^{}n].    (proj-rev(n;p)  \mmember{}  \mBbbP{}\^{}n)
Date html generated:
2017_10_05-AM-00_19_23
Last ObjectModification:
2017_06_17-AM-10_08_26
Theory : inner!product!spaces
Home
Index