Nuprl Lemma : circle-param-one-one
∀[t1,t2:ℝ]. t1 = t2 supposing req-vec(2;circle-param(t1);circle-param(t2))
Proof
Definitions occuring in Statement :
circle-param: circle-param(t),
req-vec: req-vec(n;x;y),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
circle-param: circle-param(t),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
nat: ℕ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rge: x ≥ y,
guard: {T},
rneq: x ≠ y,
or: P ∨ Q,
req_int_terms: t1 ≡ t2,
top: Top,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
lelt_wf,
req_witness,
req-vec_wf,
false_wf,
le_wf,
circle-param_wf,
real-vec_wf,
r2-unit-circle_wf,
real_wf,
square-nonneg,
trivial-rleq-radd,
int-to-real_wf,
rmul_wf,
radd_wf,
rless-int,
rless_functionality_wrt_implies,
rleq_weakening_equal,
req-rdiv2,
rsub_wf,
rless_wf,
radd-preserves-req,
req_functionality,
itermSubtract_wf,
itermAdd_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma,
req_weakening,
rmul_functionality,
radd_functionality,
req_inversion,
req-implies-req,
rmul_preserves_rless,
rmul-zero-both,
rless_functionality,
req_transitivity,
rmul-int,
rmul_preserves_req
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
because_Cache,
imageMemberEquality,
hypothesisEquality,
baseClosed,
extract_by_obid,
isectElimination,
independent_functionElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
inrFormation,
approximateComputation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
multiplyEquality
Latex:
\mforall{}[t1,t2:\mBbbR{}]. t1 = t2 supposing req-vec(2;circle-param(t1);circle-param(t2))
Date html generated:
2017_10_03-AM-10_51_55
Last ObjectModification:
2017_06_18-PM-01_24_36
Theory : reals
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