### Nuprl Lemma : strictly-decreasing-on-interval_wf

`∀[I:Interval]. ∀[f:I ⟶ℝ].  (f[x] strictly-decreasing for x ∈ I ∈ ℙ)`

Proof

Definitions occuring in Statement :  strictly-decreasing-on-interval: `f[x] strictly-decreasing for x ∈ I` rfun: `I ⟶ℝ` interval: `Interval` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` strictly-decreasing-on-interval: `f[x] strictly-decreasing for x ∈ I` prop: `ℙ` so_lambda: `λ2x.t[x]` all: `∀x:A. B[x]` implies: `P `` Q` so_apply: `x[s]` rfun: `I ⟶ℝ`
Lemmas referenced :  all_wf real_wf i-member_wf rless_wf rfun_wf interval_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin setEquality hypothesis hypothesisEquality lambdaEquality lambdaFormation setElimination rename because_Cache functionEquality applyEquality dependent_set_memberEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[I:Interval].  \mforall{}[f:I  {}\mrightarrow{}\mBbbR{}].    (f[x]  strictly-decreasing  for  x  \mmember{}  I  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-10_20_10
Last ObjectModification: 2015_12_27-PM-10_56_08

Theory : reals

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