Nuprl Lemma : accelerate-req
∀[k:ℕ+]. ∀[x:ℝ]. ((accelerate(k;x) ∈ ℝ) ∧ (accelerate(k;x) = x))
Proof
Definitions occuring in Statement :
req: x = y,
accelerate: accelerate(k;f),
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
real: ℝ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat_plus: ℕ+,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
uiff: uiff(P;Q)
Lemmas referenced :
accelerate_wf,
subtype_rel_sets,
nat_plus_wf,
regular-int-seq_wf,
real-regular,
sq_stable__regular-int-seq,
req_witness,
real_wf,
accelerate-bdd-diff,
req-iff-bdd-diff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
functionEquality,
hypothesis,
intEquality,
because_Cache,
lambdaEquality,
natural_numberEquality,
functionExtensionality,
setElimination,
rename,
independent_isectElimination,
setEquality,
lambdaFormation,
dependent_set_memberEquality,
independent_pairFormation,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
dependent_functionElimination
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[x:\mBbbR{}]. ((accelerate(k;x) \mmember{} \mBbbR{}) \mwedge{} (accelerate(k;x) = x))
Date html generated:
2017_10_02-PM-07_15_13
Last ObjectModification:
2017_09_20-PM-05_36_38
Theory : reals
Home
Index