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
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