### Nuprl Lemma : decidable__equal_nat_plus

`∀x,y:ℕ+.  Dec(x = y ∈ ℕ+)`

Proof

Definitions occuring in Statement :  nat_plus: `ℕ+` decidable: `Dec(P)` all: `∀x:A. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` nat_plus: `ℕ+` decidable: `Dec(P)` or: `P ∨ Q` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` sq_type: `SQType(T)` implies: `P `` Q` guard: `{T}` prop: `ℙ` not: `¬A` so_lambda: `λ2x.t[x]` so_apply: `x[s]` false: `False`
Lemmas referenced :  decidable__int_equal subtype_base_sq int_subtype_base not_wf equal_wf nat_plus_wf set_subtype_base less_than_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename hypothesisEquality hypothesis unionElimination inlFormation instantiate isectElimination cumulativity intEquality independent_isectElimination equalityTransitivity equalitySymmetry independent_functionElimination sqequalRule inrFormation introduction lambdaEquality natural_numberEquality voidElimination because_Cache

Latex:
\mforall{}x,y:\mBbbN{}\msupplus{}.    Dec(x  =  y)

Date html generated: 2016_05_14-AM-06_06_12
Last ObjectModification: 2015_12_26-AM-11_46_53

Theory : equality!deciders

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