Nuprl Lemma : condition-implies-le
∀[a,b,c,d:ℤ]. (a ≤ b) supposing ((c ≤ d) and ((b - a) = (d - c) ∈ ℤ))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
subtract: n - m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
le: A ≤ B,
guard: {T},
all: ∀x:A. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
le-iff-nonneg,
le_transitivity,
subtract_wf,
le_weakening,
less_than'_wf,
le_wf,
equal_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
equalitySymmetry,
natural_numberEquality,
dependent_functionElimination,
because_Cache,
intEquality,
isect_memberFormation,
introduction,
sqequalRule,
independent_pairEquality,
lambdaEquality,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
voidElimination
Latex:
\mforall{}[a,b,c,d:\mBbbZ{}]. (a \mleq{} b) supposing ((c \mleq{} d) and ((b - a) = (d - c)))
Date html generated:
2016_05_13-PM-03_31_28
Last ObjectModification:
2015_12_26-AM-09_45_56
Theory : arithmetic
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