Nuprl Lemma : wfFormAux-unique
∀[C:Type]. ∀[f:Form(C)]. ∀[b:𝔹].  ((↑(wfFormAux(f) b)) 
⇒ termForm(f) = b)
Proof
Definitions occuring in Statement : 
termForm: termForm(f)
, 
wfFormAux: wfFormAux(f)
, 
Form: Form(C)
, 
assert: ↑b
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
apply: f a
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
termForm: termForm(f)
, 
wfFormAux: wfFormAux(f)
, 
FormVar: Vname
, 
Form_ind: Form_ind, 
uimplies: b supposing a
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
true: True
, 
FormConst: Const(value)
, 
FormSet: {var | phi}
, 
or: P ∨ Q
, 
band: p ∧b q
, 
bfalse: ff
, 
false: False
, 
FormEqual: left = right
, 
bnot: ¬bb
, 
not: ¬A
, 
FormMember: element ∈ set
, 
FormAnd: left ∧ right)
, 
FormOr: left ∨ right
, 
FormNot: ¬(body)
, 
FormAll: ∀var. body
, 
FormExists: ∃var. body
, 
guard: {T}
Lemmas referenced : 
assert_wf, 
wfFormAux_wf, 
bool_wf, 
Form_wf, 
Form-induction, 
all_wf, 
equal_wf, 
termForm_wf, 
iff_imp_equal_bool, 
btrue_wf, 
true_wf, 
bool_cases_sqequal, 
band_wf, 
bfalse_wf, 
false_wf, 
assert_elim, 
bnot_wf, 
and_wf, 
btrue_neq_bfalse
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
thin, 
sqequalHypSubstitution, 
dependent_functionElimination, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
extract_by_obid, 
isectElimination, 
applyEquality, 
cumulativity, 
sqequalRule, 
lambdaEquality, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
universeEquality, 
functionEquality, 
independent_isectElimination, 
independent_pairFormation, 
natural_numberEquality, 
atomEquality, 
unionElimination, 
voidElimination, 
addLevel, 
levelHypothesis, 
dependent_set_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
applyLambdaEquality, 
setElimination, 
rename, 
productElimination
Latex:
\mforall{}[C:Type].  \mforall{}[f:Form(C)].  \mforall{}[b:\mBbbB{}].    ((\muparrow{}(wfFormAux(f)  b))  {}\mRightarrow{}  termForm(f)  =  b)
Date html generated:
2018_05_21-PM-11_27_00
Last ObjectModification:
2017_10_12-PM-05_32_12
Theory : PZF
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