Nuprl Lemma : rtan_functionality
∀x:{x:ℝ| x ∈ (-(π/2), π/2)} . ∀[y:ℝ]. rtan(x) = rtan(y) supposing x = 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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
top: Top,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
rtan: rtan(x),
rneq: x ≠ y,
or: P ∨ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rcos-positive,
member_rooint_lemma,
req_witness,
rtan_wf,
i-member_wf,
rooint_wf,
rminus_wf,
halfpi_wf,
rless_transitivity1,
rleq_weakening,
req_inversion,
rless_transitivity2,
rless_wf,
req_wf,
real_wf,
set_wf,
rdiv_wf,
rsin_wf,
rcos_wf,
int-to-real_wf,
req_weakening,
req_functionality,
rdiv_functionality,
rsin_functionality,
rcos_functionality,
rneq_functionality
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
setElimination,
rename,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
isectElimination,
dependent_set_memberEquality,
productElimination,
independent_functionElimination,
independent_isectElimination,
because_Cache,
independent_pairFormation,
productEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
inrFormation,
natural_numberEquality
Latex:
\mforall{}x:\{x:\mBbbR{}| x \mmember{} (-(\mpi{}/2), \mpi{}/2)\} . \mforall{}[y:\mBbbR{}]. rtan(x) = rtan(y) supposing x = y
Date html generated:
2018_05_22-PM-02_59_20
Last ObjectModification:
2017_10_19-PM-05_22_48
Theory : reals_2
Home
Index