Nuprl Lemma : half-pi-interval-proper
iproper((-(π/2(slower)), π/2(slower)))
Proof
Definitions occuring in Statement :
half-pi: π/2(slower),
rooint: (l, u),
iproper: iproper(I),
rminus: -(x)
Definitions unfolded in proof :
iproper: iproper(I),
right-endpoint: right-endpoint(I),
left-endpoint: left-endpoint(I),
endpoints: endpoints(I),
rooint: (l, u),
outl: outl(x),
pi1: fst(t),
pi2: snd(t),
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
i-finite_wf,
rooint_wf,
rminus_wf,
half-pi_wf,
half-pi-positive,
radd-preserves-rless,
int-to-real_wf,
radd_wf,
rmul_wf,
rless_transitivity2,
rleq_weakening_rless,
rless_functionality,
radd_functionality,
req_weakening,
rminus-as-rmul,
req_transitivity,
req_inversion,
rmul-identity1,
rmul-distrib2,
rmul_functionality,
radd-int,
rmul-zero-both,
radd-zero-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
natural_numberEquality,
productElimination,
independent_functionElimination,
minusEquality,
addEquality,
independent_isectElimination,
because_Cache,
promote_hyp
Latex:
iproper((-(\mpi{}/2(slower)), \mpi{}/2(slower)))
Date html generated:
2016_10_26-PM-00_20_23
Last ObjectModification:
2016_09_12-PM-05_42_00
Theory : reals_2
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