Nuprl Lemma : rexp-rminus
∀[x:ℝ]. (e^-(x) = (r1/e^x))
Proof
Definitions occuring in Statement :
rexp: e^x,
rdiv: (x/y),
req: x = y,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q
Lemmas referenced :
rmul_preserves_req,
rexp_wf,
rminus_wf,
rdiv_wf,
rexp-positive,
req_witness,
int-to-real_wf,
rless_wf,
real_wf,
rmul_wf,
req_functionality,
req_weakening,
rmul-rdiv-cancel2,
radd_wf,
req_wf,
req_inversion,
rexp-radd,
uiff_transitivity,
rexp_functionality,
req_transitivity,
radd_functionality,
rminus-as-rmul,
rmul-identity1,
rmul-distrib2,
rmul_functionality,
radd-int,
rmul-zero-both,
rexp0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
sqequalRule,
inrFormation,
dependent_functionElimination,
productElimination,
natural_numberEquality,
independent_functionElimination,
minusEquality,
addEquality
Latex:
\mforall{}[x:\mBbbR{}]. (e\^{}-(x) = (r1/e\^{}x))
Date html generated:
2016_10_26-PM-00_12_23
Last ObjectModification:
2016_09_12-PM-05_39_32
Theory : reals_2
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