Nuprl Lemma : formulaco-ext

`formulaco() ≡ lbl:Atom × if lbl =a "var" then Atom`
`                         if lbl =a "not" then formulaco()`
`                         if lbl =a "and" then left:formulaco() × formulaco()`
`                         if lbl =a "or" then left:formulaco() × formulaco()`
`                         if lbl =a "imp" then left:formulaco() × formulaco()`
`                         else Void`
`                         fi `

Proof

Definitions occuring in Statement :  formulaco: `formulaco()` ifthenelse: `if b then t else f fi ` eq_atom: `x =a y` ext-eq: `A ≡ B` product: `x:A × B[x]` token: `"\$token"` atom: `Atom` void: `Void`
Definitions unfolded in proof :  formulaco: `formulaco()` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` member: `t ∈ T` so_apply: `x[s]` uimplies: `b supposing a` continuous-monotone: `ContinuousMonotone(T.F[T])` and: `P ∧ Q` type-monotone: `Monotone(T.F[T])` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` strong-type-continuous: `Continuous+(T.F[T])` type-continuous: `Continuous(T.F[T])`
Lemmas referenced :  corec-ext ifthenelse_wf eq_atom_wf subtype_rel_product bool_wf eqtt_to_assert assert_of_eq_atom subtype_rel_self eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_atom subtype_rel_wf strong-continuous-depproduct continuous-constant continuous-id strong-continuous-product subtype_rel_weakening nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin sqequalRule lambdaEquality productEquality atomEquality instantiate hypothesisEquality tokenEquality hypothesis universeEquality cumulativity voidEquality independent_isectElimination independent_pairFormation isect_memberFormation because_Cache lambdaFormation unionElimination equalityElimination productElimination dependent_pairFormation equalityTransitivity equalitySymmetry promote_hyp dependent_functionElimination independent_functionElimination voidElimination axiomEquality isect_memberEquality isectEquality applyEquality functionExtensionality functionEquality

Latex:
formulaco()  \mequiv{}  lbl:Atom  \mtimes{}  if  lbl  =a  "var"  then  Atom
if  lbl  =a  "not"  then  formulaco()
if  lbl  =a  "and"  then  left:formulaco()  \mtimes{}  formulaco()
if  lbl  =a  "or"  then  left:formulaco()  \mtimes{}  formulaco()
if  lbl  =a  "imp"  then  left:formulaco()  \mtimes{}  formulaco()
else  Void
fi

Date html generated: 2018_05_21-PM-08_47_22
Last ObjectModification: 2017_07_26-PM-06_10_18

Theory : general

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