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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