Nuprl Lemma : le-add-cancel3
∀[c,d,t,t':ℤ]. uiff((c + t) ≤ (d + t');c ≤ d) supposing t = t' ∈ ℤ
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x],
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
add-zero,
zero-mul,
add-mul-special,
minus-one-mul,
add-associates,
add-is-int-iff,
add_functionality_wrt_le,
le_reflexive,
int_subtype_base,
subtype_base_sq,
equal_wf,
less_than'_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
axiomEquality,
lemma_by_obid,
isectElimination,
addEquality,
hypothesis,
voidElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
minusEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
voidEquality,
natural_numberEquality
Latex:
\mforall{}[c,d,t,t':\mBbbZ{}]. uiff((c + t) \mleq{} (d + t');c \mleq{} d) supposing t = t'
Date html generated:
2016_05_13-PM-03_31_19
Last ObjectModification:
2016_01_14-PM-06_41_22
Theory : arithmetic
Home
Index