Nuprl Lemma : lt_int_eq_false_elim_sqequal
∀[i,j:ℤ]. ¬i < j supposing i <z j ~ ff
Proof
Definitions occuring in Statement :
lt_int: i <z j,
bfalse: ff,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
int_subtype_base,
less_than_wf,
assert_of_lt_int,
assert_of_ff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
isectElimination,
hypothesisEquality,
productElimination,
independent_isectElimination,
because_Cache,
promote_hyp,
voidElimination,
lambdaEquality,
dependent_functionElimination,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[i,j:\mBbbZ{}]. \mneg{}i < j supposing i <z j \msim{} ff
Date html generated:
2016_05_13-PM-04_10_32
Last ObjectModification:
2016_01_18-PM-05_39_42
Theory : subtype_1
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