### 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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