Nuprl Lemma : realexp_functionality
∀[x1:{x:ℝ| r0 < x} ]. ∀[x2,y1,y2:ℝ]. (realexp(x1;y1) = realexp(x2;y2)) supposing ((y1 = y2) and (x1 = x2))
Proof
Definitions occuring in Statement :
realexp: realexp(x;y),
rless: x < y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
realexp: realexp(x;y),
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
req_functionality,
expr_wf,
rmul_wf,
ln_wf,
rless_wf,
int-to-real_wf,
real_wf,
req_wf,
rlog_wf,
rexp_wf,
rless_transitivity1,
rleq_weakening,
expr-req,
req_witness,
realexp_wf,
set_wf,
req_weakening,
rexp_functionality,
rmul_functionality,
ln_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
hypothesis,
natural_numberEquality,
applyEquality,
lambdaEquality,
setEquality,
sqequalRule,
independent_functionElimination,
independent_isectElimination,
productElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x1:\{x:\mBbbR{}| r0 < x\} ]. \mforall{}[x2,y1,y2:\mBbbR{}].
(realexp(x1;y1) = realexp(x2;y2)) supposing ((y1 = y2) and (x1 = x2))
Date html generated:
2017_10_04-PM-10_38_38
Last ObjectModification:
2017_06_06-AM-10_56_06
Theory : reals_2
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