Nuprl Lemma : rotate-by-zero
∀[n:ℕ]. (rotate-by(n;0) = (λx.x) ∈ (ℕn ⟶ ℕn))
Proof
Definitions occuring in Statement :
rotate-by: rotate-by(n;i),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
int_seg_wf,
rotate-by-is-id,
false_wf,
le_wf,
any_divs_zero,
iff_weakening_equal,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
functionEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
dependent_set_memberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
independent_isectElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}]. (rotate-by(n;0) = (\mlambda{}x.x))
Date html generated:
2018_05_21-PM-08_17_56
Last ObjectModification:
2017_07_26-PM-05_51_25
Theory : general
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