Nuprl Lemma : intformeq_wf

[left,right:int_term()].  (left "=" right ∈ int_formula())


Proof




Definitions occuring in Statement :  intformeq: left "=" right int_formula: int_formula() int_term: int_term() uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T int_formula: int_formula() intformeq: left "=" right eq_atom: =a y ifthenelse: if then else fi  bfalse: ff btrue: tt subtype_rel: A ⊆B ext-eq: A ≡ B and: P ∧ Q int_formulaco_size: int_formulaco_size(p) int_formula_size: int_formula_size(p) has-value: (a)↓ nat: le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: all: x:A. B[x] so_lambda: λ2x.t[x] so_apply: x[s] uimplies: supposing a
Lemmas referenced :  int_formulaco-ext int_term_wf ifthenelse_wf eq_atom_wf int_formulaco_wf false_wf le_wf nat_wf has-value_wf_base set_subtype_base int_subtype_base is-exception_wf equal_wf has-value_wf-partial set-value-type int-value-type int_formulaco_size_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut dependent_set_memberEquality introduction extract_by_obid hypothesis sqequalRule dependent_pairEquality tokenEquality hypothesisEquality thin instantiate sqequalHypSubstitution isectElimination universeEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation divergentSqle sqleReflexivity intEquality lambdaEquality independent_isectElimination because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[left,right:int\_term()].    (left  "="  right  \mmember{}  int\_formula())



Date html generated: 2017_04_14-AM-09_00_03
Last ObjectModification: 2017_02_27-PM-03_42_09

Theory : omega


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