Nuprl Lemma : intlex-cons-same
∀[l1,l2:ℤ List]. ∀[x:ℤ]. uiff(↑[x / l1] ≤_lex [x / l2];↑l1 ≤_lex l2)
Proof
Definitions occuring in Statement :
intlex: l1 ≤_lex l2,
cons: [a / b],
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
or: P ∨ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False
Lemmas referenced :
assert_witness,
intlex_wf,
or_wf,
less_than_wf,
length_wf,
and_wf,
equal_wf,
assert_wf,
cons_wf,
uiff_wf,
member_wf,
list_wf,
iff_weakening_uiff,
intlex-cons,
less_than_irreflexivity,
intlex-by-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
intEquality,
rename,
sqequalRule,
inrFormation,
because_Cache,
cumulativity,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
addLevel,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
voidElimination
Latex:
\mforall{}[l1,l2:\mBbbZ{} List]. \mforall{}[x:\mBbbZ{}]. uiff(\muparrow{}[x / l1] \mleq{}\_lex [x / l2];\muparrow{}l1 \mleq{}\_lex l2)
Date html generated:
2016_05_14-AM-06_47_47
Last ObjectModification:
2015_12_26-PM-00_24_51
Theory : list_0
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