Nuprl Lemma : proj-rev_functionality
∀[n:ℕ]. ∀[p1,p2:ℙ^n]. proj-rev(n;p1) = proj-rev(n;p2) supposing p1 = p2
Proof
Definitions occuring in Statement :
proj-rev: proj-rev(n;p),
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
exists: ∃x:A. B[x],
req-vec: req-vec(n;x;y),
nat: ℕ,
prop: ℙ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
subtype_rel: A ⊆r B,
real-proj: ℙ^n,
proj-eq: a = b,
real-vec: ℝ^n,
real-vec-mul: a*X,
proj-rev: proj-rev(n;p),
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2
Lemmas referenced :
proj-eq-iff,
proj-rev_wf,
int_seg_wf,
req-vec_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
real-vec-mul_wf,
req_witness,
rmul_wf,
real-proj_wf,
proj-eq_wf,
nat_wf,
lt_int_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_wf,
itermSubtract_wf,
itermMinus_wf,
itermMultiply_wf,
req-iff-rsub-is-0,
req_functionality,
rminus_functionality,
req_weakening,
real_polynomial_null,
int-to-real_wf,
real_term_value_sub_lemma,
real_term_value_minus_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
isectElimination,
imageElimination,
dependent_pairFormation,
lambdaFormation,
natural_numberEquality,
addEquality,
setElimination,
rename,
dependent_set_memberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
applyEquality,
because_Cache,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
equalityElimination,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p1,p2:\mBbbP{}\^{}n]. proj-rev(n;p1) = proj-rev(n;p2) supposing p1 = p2
Date html generated:
2017_10_05-AM-00_19_27
Last ObjectModification:
2017_06_17-AM-10_08_31
Theory : inner!product!spaces
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