Nuprl Lemma : intformand_wf

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


Proof




Definitions occuring in Statement :  intformand: left "∧right int_formula: int_formula() uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T int_formula: int_formula() intformand: 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) pi1: fst(t) pi2: snd(t) nat: le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: all: x:A. B[x] uimplies: supposing a so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  int_formulaco-ext int_formulaco_wf ifthenelse_wf eq_atom_wf int_term_wf add_nat_wf false_wf le_wf int_formula_size_wf nat_wf value-type-has-value set-value-type int-value-type equal_wf has-value_wf-partial int_formulaco_size_wf int_formula_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut dependent_set_memberEquality introduction extract_by_obid hypothesis sqequalRule dependent_pairEquality tokenEquality sqequalHypSubstitution setElimination thin rename hypothesisEquality instantiate isectElimination universeEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation independent_isectElimination intEquality lambdaEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

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



Date html generated: 2017_04_14-AM-09_00_07
Last ObjectModification: 2017_02_27-PM-03_42_21

Theory : omega


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