Nuprl Lemma : rtan_one_one
∀x,y:{x:ℝ| x ∈ (-(π/2), π/2)} . x = y supposing rtan(x) = rtan(y)
Proof
Definitions occuring in Statement :
rtan: rtan(x),
halfpi: π/2,
rooint: (l, u),
i-member: r ∈ I,
req: x = y,
rminus: -(x),
real: ℝ,
uimplies: b supposing a,
all: ∀x:A. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rneq: x ≠ y,
or: P ∨ Q,
guard: {T},
false: False,
stable: Stable{P},
not: ¬A
Lemmas referenced :
req_witness,
req_wf,
rtan_wf,
i-member_wf,
rooint_wf,
rminus_wf,
halfpi_wf,
set_wf,
real_wf,
stable_req,
false_wf,
or_wf,
rneq_wf,
not_wf,
rtan_functionality_wrt_rless,
req_inversion,
rless_transitivity1,
rleq_weakening,
rless_irreflexivity,
not-rneq,
minimal-double-negation-hyp-elim,
minimal-not-not-excluded-middle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
dependent_set_memberEquality,
because_Cache,
sqequalRule,
lambdaEquality,
functionEquality,
unionElimination,
independent_isectElimination,
voidElimination
Latex:
\mforall{}x,y:\{x:\mBbbR{}| x \mmember{} (-(\mpi{}/2), \mpi{}/2)\} . x = y supposing rtan(x) = rtan(y)
Date html generated:
2018_05_22-PM-02_59_46
Last ObjectModification:
2017_10_22-PM-08_21_36
Theory : reals_2
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