Nuprl Lemma : add_functionality_wrt_le
∀[i1,i2,j1,j2:ℤ]. ((i1 + i2) ≤ (j1 + j2)) supposing ((i2 ≤ j2) and (i1 ≤ j1))
Proof
Definitions occuring in Statement :
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,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
or: P ∨ Q,
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
not: ¬A,
false: False,
top: Top
Lemmas referenced :
le-iff-less-or-equal,
add-monotonic,
equal-wf-base,
int_subtype_base,
less_than_wf,
less_than'_wf,
le_wf,
add-commutes
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
addEquality,
unionElimination,
inlFormation,
independent_functionElimination,
sqequalRule,
inrFormation,
isectElimination,
because_Cache,
applyEquality,
intEquality,
baseApply,
closedConclusion,
baseClosed,
isect_memberFormation,
independent_pairEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[i1,i2,j1,j2:\mBbbZ{}]. ((i1 + i2) \mleq{} (j1 + j2)) supposing ((i2 \mleq{} j2) and (i1 \mleq{} j1))
Date html generated:
2019_06_20-AM-11_22_52
Last ObjectModification:
2018_08_17-AM-11_59_31
Theory : arithmetic
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