Nuprl Lemma : add_functionality_wrt_lt
∀[i1,i2,j1,j2:ℤ]. (i1 + i2 < j1 + j2) supposing ((i2 ≤ j2) and i1 < j1)
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
and: P ∧ Q,
uiff: uiff(P;Q),
or: P ∨ Q,
guard: {T}
Lemmas referenced :
add-monotonic,
le_wf,
less_than_wf,
member-less_than,
equal_wf,
le-iff-less-or-equal
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
isectElimination,
addEquality,
because_Cache,
intEquality,
isect_memberFormation,
sqequalRule,
isect_memberEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
lemma_by_obid,
unionElimination,
inrFormation,
inlFormation
Latex:
\mforall{}[i1,i2,j1,j2:\mBbbZ{}]. (i1 + i2 < j1 + j2) supposing ((i2 \mleq{} j2) and i1 < j1)
Date html generated:
2019_06_20-AM-11_22_54
Last ObjectModification:
2018_08_17-PM-00_00_07
Theory : arithmetic
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