### Nuprl Lemma : req-iff-bdd-diff

`∀[x,y:ℝ].  uiff(x = y;bdd-diff(x;y))`

Proof

Definitions occuring in Statement :  req: `x = y` real: `ℝ` bdd-diff: `bdd-diff(f;g)` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  req: `x = y` uall: `∀[x:A]. B[x]` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` all: `∀x:A. B[x]` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` real: `ℝ` subtype_rel: `A ⊆r B` nat: `ℕ` prop: `ℙ` bdd-diff: `bdd-diff(f;g)` exists: `∃x:A. B[x]` less_than': `less_than'(a;b)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_stable: `SqStable(P)` squash: `↓T` nat_plus: `ℕ+` less_than: `a < b` true: `True` guard: `{T}`
Lemmas referenced :  bdd-diff-regular less_than_wf real_wf bdd-diff_wf sq_stable__le all_wf le_wf false_wf nat_plus_wf nat_wf subtract_wf absval_wf less_than'_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation independent_pairFormation cut introduction sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality productElimination independent_pairEquality voidElimination lemma_by_obid isectElimination natural_numberEquality applyEquality setElimination rename hypothesis axiomEquality equalityTransitivity equalitySymmetry dependent_pairFormation dependent_set_memberEquality lambdaFormation because_Cache independent_functionElimination imageMemberEquality baseClosed imageElimination independent_isectElimination

Latex:
\mforall{}[x,y:\mBbbR{}].    uiff(x  =  y;bdd-diff(x;y))

Date html generated: 2016_05_18-AM-06_50_18
Last ObjectModification: 2016_01_17-AM-01_45_50

Theory : reals

Home Index