### Nuprl Lemma : deq_property2

[T:Type]. ∀[d:EqDecider(T)]. ∀[x,y:T].  uiff(x y ∈ T;↑(d y))

Proof

Definitions occuring in Statement :  deq: EqDecider(T) assert: b uiff: uiff(P;Q) uall: [x:A]. B[x] apply: a universe: Type equal: t ∈ T
Definitions unfolded in proof :  deq: EqDecider(T) uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a implies:  Q all: x:A. B[x] sq_stable: SqStable(P) squash: T prop: so_lambda: λ2x.t[x] so_apply: x[s] iff: ⇐⇒ Q rev_implies:  Q guard: {T}
Lemmas referenced :  iff_wf all_wf bool_wf set_wf equal_wf assert_witness decidable__assert assert_wf sq_stable_from_decidable
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut independent_pairFormation setElimination thin rename lemma_by_obid sqequalHypSubstitution isectElimination applyEquality hypothesisEquality hypothesis independent_functionElimination dependent_functionElimination imageMemberEquality baseClosed imageElimination productElimination independent_pairEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry axiomEquality functionEquality lambdaEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[d:EqDecider(T)].  \mforall{}[x,y:T].    uiff(x  =  y;\muparrow{}(d  x  y))

Date html generated: 2016_05_14-AM-06_06_23
Last ObjectModification: 2016_01_14-PM-07_31_48

Theory : equality!deciders

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