Nuprl Lemma : proj-eq-equiv
∀[n:ℕ]. EquivRel(ℙ^n;a,b.a = b)
Proof
Definitions occuring in Statement :
proj-eq: a = b,
real-proj: ℙ^n,
equiv_rel: EquivRel(T;x,y.E[x; y]),
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
proj-eq: a = b,
real-proj: ℙ^n,
real-vec: ℝ^n,
uimplies: b supposing a,
nat: ℕ,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
squash: ↓T,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_weakening,
rmul_wf,
int_seg_wf,
real-proj_wf,
proj-eq_wf,
req_witness,
nat_wf,
all_wf,
req_wf,
squash_wf,
exists_wf,
real_wf,
rneq_wf,
int-to-real_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_functionality,
proj-eq-iff,
sym_functionality_wrt_iff,
req-vec_functionality,
req-vec_weakening,
rmul-neq-zero,
real-vec-mul-mul,
real-vec-mul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
natural_numberEquality,
addEquality,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
setEquality,
dependent_set_memberEquality,
unionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
imageMemberEquality,
baseClosed,
addLevel,
allFunctionality,
existsFunctionality
Latex:
\mforall{}[n:\mBbbN{}]. EquivRel(\mBbbP{}\^{}n;a,b.a = b)
Date html generated:
2017_10_05-AM-00_18_26
Last ObjectModification:
2017_06_17-AM-10_07_38
Theory : inner!product!spaces
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