Nuprl Lemma : assert-slow-int-palindrome-test
∀[L:ℤ List]. uiff(↑slow-int-palindrome-test(L);rev(L) = L ∈ (ℤ List))
Proof
Definitions occuring in Statement :
slow-int-palindrome-test: slow-int-palindrome-test(L),
reverse: rev(as),
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
slow-int-palindrome-test: slow-int-palindrome-test(L),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal-wf-base,
list_wf,
list_subtype_base,
int_subtype_base,
iff_weakening_uiff,
assert_wf,
list-deq_wf,
int-deq_wf,
deq_wf,
reverse_wf,
deq_property,
assert_witness,
uiff_wf,
slow-int-palindrome-test_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
equalitySymmetry,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
because_Cache,
addLevel,
productElimination,
lambdaEquality,
setElimination,
rename,
independent_functionElimination,
cumulativity,
instantiate,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity
Latex:
\mforall{}[L:\mBbbZ{} List]. uiff(\muparrow{}slow-int-palindrome-test(L);rev(L) = L)
Date html generated:
2018_05_21-PM-09_02_04
Last ObjectModification:
2017_07_26-PM-06_25_04
Theory : general
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