Nuprl Lemma : inv-sinh_functionality
∀[x,y:ℝ]. inv-sinh(x) = inv-sinh(y) supposing x = y
Proof
Definitions occuring in Statement :
inv-sinh: inv-sinh(x),
req: x = y,
real: ℝ,
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],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
inv-sinh: inv-sinh(x),
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
inv-sinh-domain,
req_witness,
inv-sinh_wf,
req_wf,
real_wf,
radd_wf,
rmul_wf,
int-to-real_wf,
rleq_wf,
ln_functionality,
rsqrt_wf,
rless_wf,
req_weakening,
req_functionality,
radd_functionality,
rsqrt_functionality,
rmul_functionality,
req_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
natural_numberEquality,
productElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
independent_isectElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. inv-sinh(x) = inv-sinh(y) supposing x = y
Date html generated:
2017_10_04-PM-10_43_08
Last ObjectModification:
2017_06_24-AM-10_46_02
Theory : reals_2
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