Nuprl Lemma : int-palindrome-test-sq
∀[L:ℤ List]. (int-palindrome-test(L) ~ palindrome-test(IntDeq;L))
Proof
Definitions occuring in Statement :
int-palindrome-test: int-palindrome-test(L),
palindrome-test: palindrome-test(eq;L),
list: T List,
int-deq: IntDeq,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-palindrome-test: int-palindrome-test(L),
palindrome-test: palindrome-test(eq;L),
taba: taba(init;x,x',a.F[x; x'; a];l),
pi1: fst(t),
list_ind: list_ind,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
int-deq: IntDeq,
eq_int: (i =z j),
btrue: tt,
it: ⋅,
bfalse: ff
Lemmas referenced :
list_wf,
lifting-strict-int_eq,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-decide
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
intEquality
Latex:
\mforall{}[L:\mBbbZ{} List]. (int-palindrome-test(L) \msim{} palindrome-test(IntDeq;L))
Date html generated:
2016_05_15-PM-07_37_39
Last ObjectModification:
2016_01_16-AM-09_35_25
Theory : general
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