Nuprl Lemma : add-positive-nonneg
∀[x,y:ℤ]. (0 < x + y) supposing (0 < x and (0 ≤ y))
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A
Lemmas referenced :
less_than_wf,
member-less_than,
le_wf,
add-monotonic,
less-trichotomy,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
addEquality,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
inrFormation,
baseClosed,
applyEquality,
inlFormation,
voidElimination,
imageElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbZ{}]. (0 < x + y) supposing (0 < x and (0 \mleq{} y))
Date html generated:
2019_06_20-AM-11_22_38
Last ObjectModification:
2018_08_17-AM-11_57_33
Theory : arithmetic
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