Nuprl Lemma : int_seg_equality
∀[m,n:ℤ]. ∀[x:{m..n-}]. ∀y:ℤ. x = y ∈ {m..n-} supposing x = y ∈ ℤ
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
and_wf,
le_wf,
less_than_wf,
equal_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
intEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[m,n:\mBbbZ{}]. \mforall{}[x:\{m..n\msupminus{}\}]. \mforall{}y:\mBbbZ{}. x = y supposing x = y
Date html generated:
2016_05_13-PM-03_32_50
Last ObjectModification:
2015_12_26-AM-09_45_05
Theory : arithmetic
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