### Nuprl Lemma : bar-delay-equal

`∀[T:Type]. ∀x:bar-base(T). bar-equal(T;x;bar-delay(x))`

Proof

Definitions occuring in Statement :  bar-equal: `bar-equal(T;x;y)` bar-delay: `bar-delay(b)` bar-base: `bar-base(T)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` bar-equal: `bar-equal(T;x;y)` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` bar-converges: `x↓a` exists: `∃x:A. B[x]` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q` nat: `ℕ` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` sq_stable: `SqStable(P)` squash: `↓T` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` bar-delay: `bar-delay(b)` bar-val: `bar-val(n;x)` exposed-bfalse: `exposed-bfalse` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` guard: `{T}` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b`
Lemmas referenced :  bar-converges_wf bar-delay_wf bar-base_wf decidable__le false_wf not-le-2 sq_stable__le condition-implies-le minus-add minus-one-mul zero-add minus-one-mul-top add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel le_wf equal_wf unit_wf2 bar-val_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int le_antisymmetry_iff eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int add-subtract-cancel int_subtype_base assert_wf bnot_wf not_wf equal-wf-T-base bool_cases iff_transitivity iff_weakening_uiff assert_of_bnot subtract_wf not-equal-2 minus-zero minus-minus
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation independent_pairFormation sqequalHypSubstitution productElimination thin cut introduction extract_by_obid isectElimination cumulativity hypothesisEquality hypothesis universeEquality dependent_pairFormation dependent_set_memberEquality addEquality setElimination rename natural_numberEquality dependent_functionElimination unionElimination voidElimination independent_functionElimination independent_isectElimination sqequalRule imageMemberEquality baseClosed imageElimination applyEquality lambdaEquality isect_memberEquality voidEquality intEquality because_Cache minusEquality unionEquality inlEquality equalityElimination equalityTransitivity equalitySymmetry promote_hyp instantiate applyLambdaEquality impliesFunctionality

Latex:
\mforall{}[T:Type].  \mforall{}x:bar-base(T).  bar-equal(T;x;bar-delay(x))

Date html generated: 2017_04_14-AM-07_46_11
Last ObjectModification: 2017_02_27-PM-03_16_35

Theory : co-recursion

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