Nuprl Lemma : le_witness_for_triv
∀[i,j:ℤ]. <λx.Ax, Ax, Ax> ∈ i ≤ j supposing i ≤ j
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
member: t ∈ T,
lambda: λx.A[x],
pair: <a, b>,
int: ℤ,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
top: Top,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
member-not,
less_than'_wf,
istype-void,
istype-le,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
independent_pairEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination,
Error :lambdaFormation_alt,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
productElimination,
independent_functionElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. <\mlambda{}x.Ax, Ax, Ax> \mmember{} i \mleq{} j supposing i \mleq{} j
Date html generated:
2019_06_20-AM-11_22_25
Last ObjectModification:
2018_10_27-PM-10_32_52
Theory : arithmetic
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