### Nuprl Lemma : intformimplies_wf

`∀[left,right:int_formula()].  (left "=>" right ∈ int_formula())`

Proof

Definitions occuring in Statement :  intformimplies: `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()` intformimplies: `left "=>" right` eq_atom: `x =a y` ifthenelse: `if b then t else f fi ` bfalse: `ff` btrue: `tt` subtype_rel: `A ⊆r 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: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` all: `∀x:A. B[x]` uimplies: `b supposing a` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  int_formulaco-ext ifthenelse_wf eq_atom_wf int_term_wf int_formulaco_wf add_nat_wf istype-void le_wf int_formula_size_wf value-type-has-value nat_wf set-value-type istype-int int-value-type has-value_wf-partial int_formulaco_size_wf int_formula_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  cut Error :dependent_set_memberEquality_alt,  introduction extract_by_obid hypothesis sqequalRule Error :dependent_pairEquality_alt,  tokenEquality sqequalHypSubstitution setElimination thin rename because_Cache Error :inhabitedIsType,  hypothesisEquality Error :universeIsType,  instantiate isectElimination universeEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation Error :lambdaFormation_alt,  independent_isectElimination intEquality Error :lambdaEquality_alt,  Error :equalityIsType1,  equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

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

Date html generated: 2019_06_20-PM-00_46_24
Last ObjectModification: 2018_10_03-AM-00_45_49

Theory : omega

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