Nuprl Lemma : ite_rw_false

[T:Type]. ∀[b:𝔹]. ∀[x,y:T].  if then else fi  y ∈ supposing ¬↑b


Proof




Definitions occuring in Statement :  assert: b ifthenelse: if then else fi  bool: 𝔹 uimplies: supposing a uall: [x:A]. B[x] not: ¬A universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  not: ¬A false: False bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b
Lemmas referenced :  bool_wf eqtt_to_assert eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot not_wf assert_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut hypothesisEquality thin extract_by_obid hypothesis lambdaFormation sqequalHypSubstitution unionElimination equalityElimination isectElimination because_Cache productElimination independent_isectElimination sqequalRule independent_functionElimination voidElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity equalityTransitivity equalitySymmetry Error :universeIsType,  isect_memberEquality axiomEquality Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[b:\mBbbB{}].  \mforall{}[x,y:T].    if  b  then  x  else  y  fi    =  y  supposing  \mneg{}\muparrow{}b



Date html generated: 2019_06_20-AM-11_31_39
Last ObjectModification: 2018_09_26-AM-11_28_07

Theory : bool_1


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