Nuprl Lemma : realexp_wf
∀[x:{x:ℝ| r0 < x} ]. ∀[y:ℝ]. (realexp(x;y) ∈ ℝ)
Proof
Definitions occuring in Statement :
realexp: realexp(x;y),
rless: x < y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
realexp: realexp(x;y),
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
expr_wf,
rmul_wf,
ln_wf,
rless_wf,
int-to-real_wf,
real_wf,
req_wf,
rlog_wf,
rexp_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
dependent_set_memberEquality,
hypothesis,
natural_numberEquality,
applyEquality,
lambdaEquality,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 < x\} ]. \mforall{}[y:\mBbbR{}]. (realexp(x;y) \mmember{} \mBbbR{})
Date html generated:
2017_10_04-PM-10_38_34
Last ObjectModification:
2017_06_06-AM-10_40_22
Theory : reals_2
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