Nuprl Lemma : lt_int_eq_false_elim
∀[i,j:ℤ]. ¬i < j supposing i <z j = ff
Proof
Definitions occuring in Statement :
lt_int: i <z j,
bfalse: ff,
bool: 𝔹,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
guard: {T},
uiff: uiff(P;Q)
Lemmas referenced :
less_than_wf,
equal_wf,
bool_wf,
lt_int_wf,
bfalse_wf,
assert_wf,
le_int_wf,
le_wf,
bnot_wf,
less_than_transitivity1,
less_than_irreflexivity,
uiff_transitivity,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. \mneg{}i < j supposing i <z j = ff
Date html generated:
2016_05_13-PM-04_01_57
Last ObjectModification:
2015_12_26-AM-10_56_51
Theory : int_1
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