Nuprl Lemma : rfun-eq_transitivity
∀[I:Interval]. ∀[f,g,h:I ⟶ℝ]. (rfun-eq(I;f;h)) supposing (rfun-eq(I;g;h) and rfun-eq(I;f;g))
Proof
Definitions occuring in Statement :
rfun-eq: rfun-eq(I;f;g),
rfun: I ⟶ℝ,
interval: Interval,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rfun-eq: rfun-eq(I;f;g),
all: ∀x:A. B[x],
guard: {T},
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
interval_wf,
rfun_wf,
rfun-eq_wf,
req_witness,
i-member_wf,
real_wf,
sq_stable__i-member,
r-ap_wf,
req_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
lemma_by_obid,
isectElimination,
setElimination,
rename,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
setEquality,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:Interval]. \mforall{}[f,g,h:I {}\mrightarrow{}\mBbbR{}]. (rfun-eq(I;f;h)) supposing (rfun-eq(I;g;h) and rfun-eq(I;f;g))
Date html generated:
2016_05_18-AM-08_42_40
Last ObjectModification:
2016_01_17-AM-02_26_28
Theory : reals
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