Nuprl Lemma : decidable__equal_int_seg
∀i,j:ℤ. ∀x,y:{i..j-}. Dec(x = y ∈ {i..j-})
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
decidable: Dec(P),
all: ∀x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
or: P ∨ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
not: ¬A,
implies: P ⇒ Q,
squash: ↓T,
false: False
Lemmas referenced :
int_seg_wf,
equal_wf,
not_wf,
lelt_wf,
decidable__int_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
inlFormation,
dependent_set_memberEquality,
productElimination,
isectElimination,
inrFormation,
applyEquality,
lambdaEquality,
imageMemberEquality,
baseClosed,
equalityUniverse,
levelHypothesis,
introduction,
independent_functionElimination,
voidElimination,
intEquality
Latex:
\mforall{}i,j:\mBbbZ{}. \mforall{}x,y:\{i..j\msupminus{}\}. Dec(x = y)
Date html generated:
2016_05_13-PM-04_02_05
Last ObjectModification:
2016_01_14-PM-07_24_38
Theory : int_1
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