Nuprl Lemma : r-ap_functionality
∀[I:Interval]. ∀[f,g:I ⟶ℝ]. ∀[x:{x:ℝ| x ∈ I} ]. f(x) = g(x) supposing rfun-eq(I;f;g)
Proof
Definitions occuring in Statement :
rfun-eq: rfun-eq(I;f;g),
r-ap: f(x),
rfun: I ⟶ℝ,
i-member: r ∈ I,
interval: Interval,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
r-ap: f(x),
rfun-eq: rfun-eq(I;f;g),
rfun: I ⟶ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
req_witness,
all_wf,
real_wf,
i-member_wf,
req_wf,
set_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
independent_functionElimination,
hypothesis,
setEquality,
lambdaEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
dependent_functionElimination
Latex:
\mforall{}[I:Interval]. \mforall{}[f,g:I {}\mrightarrow{}\mBbbR{}]. \mforall{}[x:\{x:\mBbbR{}| x \mmember{} I\} ]. f(x) = g(x) supposing rfun-eq(I;f;g)
Date html generated:
2016_05_18-AM-08_42_52
Last ObjectModification:
2015_12_27-PM-11_50_21
Theory : reals
Home
Index