Nuprl Lemma : rneq-inv-sinh
∀x,y:ℝ. (inv-sinh(x) ≠ inv-sinh(y) ⇒ x ≠ y)
Proof
Definitions occuring in Statement :
inv-sinh: inv-sinh(x),
rneq: x ≠ y,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ
Lemmas referenced :
rneq-function,
inv-sinh_wf,
real_wf,
req_functionality,
inv-sinh_functionality,
req_weakening,
req_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
sqequalRule,
lambdaEquality,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
lambdaFormation,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}x,y:\mBbbR{}. (inv-sinh(x) \mneq{} inv-sinh(y) {}\mRightarrow{} x \mneq{} y)
Date html generated:
2017_10_04-PM-10_43_12
Last ObjectModification:
2017_06_26-PM-05_07_57
Theory : reals_2
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