Nuprl Lemma : le_weakening2
∀a,b:ℤ. a ≤ b supposing a < b
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
le: A ≤ B,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q
Lemmas referenced :
le-iff-less-or-equal,
less_than'_wf,
less_than_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
independent_pairEquality,
lambdaEquality,
voidElimination,
isectElimination,
axiomEquality,
intEquality,
inlFormation
Latex:
\mforall{}a,b:\mBbbZ{}. a \mleq{} b supposing a < b
Date html generated:
2016_05_13-PM-03_30_42
Last ObjectModification:
2015_12_26-AM-09_46_49
Theory : arithmetic
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