Nuprl Lemma : itermAdd_wf

[left,right:int_term()].  (left (+) right ∈ int_term())


Proof




Definitions occuring in Statement :  itermAdd: left (+) right 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_term: int_term() itermAdd: 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_termco_size: int_termco_size(p) int_term_size: int_term_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_termco-ext int_termco_wf ifthenelse_wf eq_atom_wf add_nat_wf false_wf le_wf int_term_size_wf nat_wf value-type-has-value set-value-type int-value-type equal_wf has-value_wf-partial int_termco_size_wf int_term_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 intEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation independent_isectElimination lambdaEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

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



Date html generated: 2017_04_14-AM-08_56_34
Last ObjectModification: 2017_02_27-PM-03_40_07

Theory : omega


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